{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2025-12-14T01:33:56.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2025-12-14T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":56150,"title":"Ordinary Annuity : Periodic Payment (Present Value)","description":"Theorem : Present Value of an Ordinary Annuity\r\n\r\nwhere;\r\nP : Present value of all payments\r\nA : Periodic payment\r\nr : Interest rate per period\r\nn : Number of periods (peyments)\r\nCalculate A, given P, r and n. Round to the nearest cent. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 230.377px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.997px 115.188px; transform-origin: 406.997px 115.188px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eTheorem : Present Value of an Ordinary Annuity\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 37.6379px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 18.8189px; text-align: left; transform-origin: 383.996px 18.8189px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-16px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"116\" height=\"37.5\" style=\"width: 116px; height: 37.5px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ewhere;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7555px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 390.993px 40.8778px; transform-origin: 390.998px 40.8778px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eP : Present value of all payments\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eA : Periodic payment\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003er : Interest rate per period\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003en : Number of periods (peyments)\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eCalculate A, given P, r and n. Round to the nearest cent. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function A = annuityPPayment(P,r,n)\r\n\r\nend","test_suite":"%%\r\nP = 1500;\r\nr = 0.07;\r\nn = 20;\r\nA = 141.59;\r\nassert(abs(annuityPPayment(P,r,n) - A )\u003c= 1e-2)\r\n\r\n%%\r\nP = 1e6;\r\nr = 0.005;\r\nn = 240;\r\nA = 7164.31;\r\nassert(abs(annuityPPayment(P,r,n) - A )\u003c= 1e-2)\r\n\r\n%%\r\nP = 50000;\r\nr = 0.1;\r\nn = 3;\r\nA = 20105.74;\r\nassert(abs(annuityPPayment(P,r,n) - A )\u003c= 1e-2)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":8703,"edited_by":8703,"edited_at":"2022-10-01T16:32:47.000Z","deleted_by":null,"deleted_at":null,"solvers_count":36,"test_suite_updated_at":"2022-10-01T16:32:47.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-09-30T08:07:42.000Z","updated_at":"2026-02-09T13:35:50.000Z","published_at":"2022-09-30T16:53:42.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTheorem : Present Value of an Ordinary Annuity\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eP = A \\\\frac{(1+r)^n-1}{r (1+r)^n}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eP : Present value of all payments\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA : Periodic payment\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003er : Interest rate per period\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003en : Number of periods (peyments)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate A, given P, r and n. Round to the nearest cent. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":56100,"title":"Compound Interest: Present Value","description":"Theorem : Compound Interest\r\n\r\nwhere,\r\nF : Future value at the end of n periods\r\nP : Present value\r\nr : Annual nominal rate\r\nn : Total number of compounding periods\r\nCalculate P, given F, r and n. Round to the nearest cent.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 213.741px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.997px 106.87px; transform-origin: 406.997px 106.87px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eTheorem : Compound Interest\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"89\" height=\"19.5\" style=\"width: 89px; height: 19.5px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ewhere,\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7555px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 390.993px 40.8778px; transform-origin: 390.998px 40.8778px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eF : Future value at the end of n periods\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eP : Present value\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003er : Annual nominal rate\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003en : Total number of compounding periods\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eCalculate P, given F, r and n. Round to the nearest cent.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function P = compoundPresent(F,r,n)\r\n\r\nend","test_suite":"%%\r\nF = 100;\r\nr = 0.07;\r\nn = 5;\r\nP = 71.30;\r\nassert(abs(compoundPresent(F,r,n)-P)\u003c=1e-2)\r\n\r\n%%\r\nF = 200;\r\nr = 0.045;\r\nn = 14;\r\nP = 107.99;\r\nassert(abs(compoundPresent(F,r,n)-P)\u003c=1e-2)\r\n\r\n\r\n%%\r\nF = 184.74;\r\nr = 0.018;\r\nn = 5;\r\nP = 168.97;\r\nassert(abs(compoundPresent(F,r,n)-P)\u003c=1e-2)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":8703,"edited_by":8703,"edited_at":"2022-10-01T16:50:48.000Z","deleted_by":null,"deleted_at":null,"solvers_count":54,"test_suite_updated_at":"2022-10-01T16:49:27.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-09-30T05:16:46.000Z","updated_at":"2026-04-02T11:11:35.000Z","published_at":"2022-09-30T16:56:20.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTheorem : Compound Interest\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eF = P(1+r)^n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eF : Future value at the end of n periods\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eP : Present value\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003er : Annual nominal rate\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003en : Total number of compounding periods\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate P, given F, r and n. Round to the nearest cent.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":56090,"title":"Simple Interest : Calculate time in years","description":"Theorem : Simple Interest\r\n\r\nwhere;\r\nF : Future Value\r\nP : Present Value\r\nr : Annual simple interest rate (decimal)\r\nt : Time in years\r\nCalculate t, given F, P and r. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 213.741px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.997px 106.87px; transform-origin: 406.997px 106.87px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eTheorem : Simple Interest\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAALAAAAAlCAYAAADiHGOuAAAAAXNSR0IArs4c6QAAB5VJREFUeF7tnHnIfUUZxz9WlCIVZqKmUFBhoqQR2qYtUJllheKWpuZaoe1WWpmllkullJj7H+655ZJUKuJeEBWZ2qIFSqFEVi6llZrxgWdqPO85Z865773c9/zumX9+v3vPzJyZZ77zLN/nue9qjG2UwIAlsNqA1z4ufZQAI4BHEAxaAiOAB3184+JHAI8YGLQERgDP/vheALwKuB74z+xfN+g3bAw8C7i96y5GAHeV1GT9Xg58BPgK8KfJplioUc8BDgJ+BfwQeKq0+xKAXwbsAGwHbF2arPL8Q8CpPcfMq/t6wJ6FfT4C/AK4ETgf+E1BwBsBnwS+2BG8awP7AM8OwM9LFvN+rxrYS698iyAuATht5g3ALfHBg9ylZnIF/wrgEOB9wJuAm+YtjZ7vXyfA+dYYJ/iOAx4HXgp8IYCuDPz+G8BjNe9wnm/GBRbwbU3gfiAO7cUB+CN7rntV6678jgW+Bvy6bXNdAfzG0DzO5a3YA3igYeIt4/A8lN8OTLIvAs4D3gzcD7wb+Fm2h7WAM4Ht47v3R/98m88Mzas5PAZ4okEGPt8LWDf8vk8Azx0B/D9pibkD4mL/rQlHXQH8QeCUmORo4DDgyYZJNZ1qqo8CjS9eocB+NfA9YP2WiyrQjo/1nwF8DHg0288mwInAhwsXWKDblGOu+dX6s9DA7u2rwE/CRfnnnM9AV0ErrVv2l5q1eMG1cr8MpVG73C4AXgM4ARDEtvcCV7ZsXn/y9cBVwL/nLKS+r98dOLdwUfM+VwN+TgcgKA8Pjdp2yavr0o1Q828zQw2c3EDjEi9hnevTV16T9hd37wT2B/ZrseZvAz4TbpsWcUnrAmD9MoMWQXlb+L9Dcw26CFofXpPv4dp2BS6sGZgD+BzgQECf2JZk9SXg2i4vjT6LBGAx9w7g5MBV20VPLp0W7buTAthbcE0Mrh6YX6uhjwA0p0MGdu7/3g3sGOYrl5vC/3xm4hW+FFmie94TGlTw/24E8BIJrBmulW6S/n7Jmq8egfK/ghxYYtFLGrh0YK7w7RHUSBnN0yz1wEttV03sD0Kwl4Rpe6jScwPAS/wW4N4A+U+jj+6Dvqvcr2axOrZtfUPUwCquTWO/mwOvBXSp9LNfCHwc2Bu4APhy/F/gmtipts8BxlZ1TYuou7Eb8OdqhxKAnx+aVW1kexfwY+AZoXn12T4ddIfR+XKa2kxNvpy2HBcnD86qmtU1qTGkdgzOdBnkKvWXUzDr85PCn5NK7OP/DxHAulziwzxBCvBVZneFHMSKLT+TXCHWWfO6s9eqfb3BIhar0V4JqI3UKk2tydz2BeI8AZzAJz1o81+1se15gJSOvu4W4SapUS6uUGSJSZD77ssiDBHA6XzVvLqYpn+VkZb4rGByvh0Wy0DsHwF4XU0Vov0kB0otBZ+1eYWSBjZh8Z14QzV6lWrSXGg680CmtKCV+Fzqz4BtM+CvoUWkwwR2ysD9Hvh+mMmHazaR5jA46ZuBHDKAU1Cr/JTRPWG169LAuUJUW3cJdNMF0fLJ1DyttQE4+XSHxoi61LBa8+8db9JKBG5ak2bqivjQ1bRV95MAbPZoiaALm58GgPNLuBxZ9+Ghc+bGYiUD14OBugvumhLYfxQ+rXFEqbXKtQ3AOuIeppRHXVYqcZ4efJ6tKi1opT2vXtSupm0EMFQzl7IvTeUDuZz7cNETA7iUlRL8Fvv8ceDsQ35RdRe2BW6d4JYtoguRMzffiqSDlFddy+Xcp9Ar+cC1vHybBu6TPp7gvJcMmVcQl1/UG8LM3TfBhhYxiEvMjRff+pDrWuSW5GyXao1Jm7gTgLeqUyxNAK6mj+uKViY449Yh8wJwflGNivtSYGlTi0aj5czNZcC+hdqXJOdSMVgVJPrNnwV2jhLLTkFcnj6eFk02bcBPY75pXtTEccpkLEIiIw8aSy5BLuekJF4TLI/MTluTRFALS20uKQ5r0sB5+rgpKzUNAM17jmlfVOUmCyH92CetPg0WoiTLaRfzJOami4LLgz2t+c+jVNLCpybGwv0kLS81J/e+pAKyDsCWsZnf/1RIpK5ksCSsITx375onmRabRHytmeqxGbnxs6NQpbb4pGEufzMnj2rCqBQM9VjO07pOE8A5o9BFwSUuV0CKrQ0jdVy65Gp5KUldiFr/Ogewi5Iys8h6p2zrOuiWRhrgXAQ8OKkEV9A4zbw/IbLoPs/N3wxcHpmkuhrV0haUp4GNmt3sU1NE7jzK+3WRnvcXLI6xKW/BLK8qG9KFKy2ty+fTBHDOKHShHWWrTDd7US+NTOUfOixav9pyBf3n2tryUiauwzvGLhUJvCQycVatpUKflSCklVbQXpKJv345DTg9q4ZcMmYEcEmM/Z8rUzWq2sZfprRp4f6zL84I3TtdDy1ZY5XjCODZAMKo28o1U6aplmQ2b1o1Z/XvQxwVcZgBXGMbATw7AOhbG3wYJN4xu9escjP3ktsI4Nmev4chmyMjMeR6kdlK6f+zJ3n5E7Y7u7x0BHAXKS2vj7Sk9JpsQvEvzSzvVYMfLb2mv9uZARoBPPgzX+wNjABe7PMf/O5HAA/+CBd7AyOAF/v8B7/7/wKA0+k1FQ3SuwAAAABJRU5ErkJggg==\" width=\"88\" height=\"18.5\" style=\"width: 88px; height: 18.5px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ewhere;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7555px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 390.993px 40.8778px; transform-origin: 390.998px 40.8778px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eF : Future Value\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eP : Present Value\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003er : Annual simple interest rate (decimal)\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003et : Time in years\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eCalculate t, given F, P and r. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function t = simpleMaturity(F,P,r)\r\n\r\nend","test_suite":"%%\r\nF = 365;\r\nP = 100;\r\nr = 0.04;\r\nt = 66.25;\r\nassert(abs(simpleMaturity(F,P,r) - t) \u003c= 1e-2)\r\n\r\n%%\r\nF = 740;\r\nP = 500;\r\nr = 0.078;\r\nt = 6.15;\r\nassert(abs(simpleMaturity(F,P,r) - t )\u003c= 1e-2)\r\n\r\n\r\n%%\r\nF = 1400;\r\nP = 700;\r\nr = 0.014;\r\nt = 71.43;\r\nassert(abs(simpleMaturity(F,P,r) - t )\u003c= 1e-2)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":8703,"edited_by":8703,"edited_at":"2022-10-01T16:21:48.000Z","deleted_by":null,"deleted_at":null,"solvers_count":54,"test_suite_updated_at":"2022-10-01T16:21:48.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-09-29T18:52:22.000Z","updated_at":"2026-02-09T13:47:06.000Z","published_at":"2022-09-30T16:56:51.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTheorem : Simple Interest\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eF = P(1+rt)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eF : Future Value\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eP : Present Value\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003er : Annual simple interest rate (decimal)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003et : Time in years\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate t, given F, P and r. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":56075,"title":"Simple Interest : Calculate Future Value","description":"Theorem : Simple Interest\r\n\r\nwhere;\r\nF : Future Value\r\nP : Present Value\r\nr : Annual simple interest rate (decimal)\r\nt : Time in years\r\nCalculate F, given P, r and t. Round to nearest cent.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 213.741px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.997px 106.87px; transform-origin: 406.997px 106.87px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eTheorem : Simple Interest\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"88\" height=\"18.5\" style=\"width: 88px; height: 18.5px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ewhere;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7555px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 390.993px 40.8778px; transform-origin: 390.998px 40.8778px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eF : Future Value\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eP : Present Value\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003er : Annual simple interest rate (decimal)\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003et : Time in years\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eCalculate F, given P, r and t. Round to nearest cent.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function F = simpleFuture(P,r,t)\r\n \r\nend","test_suite":"%%\r\nP = 100;\r\nr = 0.12;\r\nt = 5;\r\ny_correct = 160;\r\nassert(abs( simpleFuture(P,r,t)-y_correct ) \u003c=1e-2)\r\n\r\n%%\r\nP = 140;\r\nr = 0.055;\r\nt = 3;\r\ny_correct = 163.1;\r\nassert(abs(simpleFuture(P,r,t)-y_correct)\u003c=1e-2)\r\n\r\n\r\n%%\r\nP = 12000;\r\nr = 0.045;\r\nt = 4;\r\ny_correct = 14160;\r\nassert(abs(simpleFuture(P,r,t)-y_correct)\u003c=1e-2)","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":8703,"edited_by":8703,"edited_at":"2022-10-01T16:18:34.000Z","deleted_by":null,"deleted_at":null,"solvers_count":50,"test_suite_updated_at":"2022-10-01T16:18:34.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-09-29T18:10:06.000Z","updated_at":"2026-03-30T22:48:20.000Z","published_at":"2022-09-30T16:57:41.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTheorem : Simple Interest\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eF = P(1+rt)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eF : Future Value\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eP : Present Value\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003er : Annual simple interest rate (decimal)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003et : Time in years\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate F, given P, r and t. Round to nearest cent.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":56095,"title":"Compound Interest : Future Value","description":"Theorem : Compound Interest\r\n\r\nwhere,\r\nF : Future value at the end of n periods\r\nP : Present value\r\nr : Annual nominal rate\r\nn : Total number of compounding periods\r\nCalculate F, given P, r and n. Round to the nearest cent.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 213.741px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.997px 106.87px; transform-origin: 406.997px 106.87px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eTheorem : Compound Interest\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"89\" height=\"19.5\" style=\"width: 89px; height: 19.5px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ewhere,\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7555px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 390.993px 40.8778px; transform-origin: 390.998px 40.8778px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eF : Future value at the end of n periods\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eP : Present value\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003er : Annual nominal rate\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003en : Total number of compounding periods\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eCalculate F, given P, r and n. Round to the nearest cent.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function F = compoundFuture(P,r,n)\r\n\r\nend","test_suite":"%%\r\nP = 100;\r\nr = 0.05;\r\nn = 30;\r\nF = 432.19;\r\nassert(abs(compoundFuture(P,r,n)-F)\u003c=1e-2)\r\n\r\n%%\r\nP = 850;\r\nr = 0.039;\r\nn = 14;\r\nF = 1452.23;\r\nassert(abs(compoundFuture(P,r,n)-F)\u003c=1e-2)\r\n\r\n%%\r\nP = 10000;\r\nr = 0.014;\r\nn = 12;\r\nF = 11815.59;\r\nassert(abs(compoundFuture(P,r,n)-F)\u003c=1e-2)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":8703,"edited_by":8703,"edited_at":"2022-10-01T16:22:56.000Z","deleted_by":null,"deleted_at":null,"solvers_count":79,"test_suite_updated_at":"2022-10-01T16:22:56.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-09-30T05:07:26.000Z","updated_at":"2026-02-06T15:37:13.000Z","published_at":"2022-09-30T16:56:35.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTheorem : Compound Interest\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eF = P(1+r)^n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eF : Future value at the end of n periods\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eP : Present value\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003er : Annual nominal rate\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003en : Total number of compounding periods\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate F, given P, r and n. Round to the nearest cent.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":56145,"title":"Ordinary Annuity : Present Value","description":"Theorem : Present Value of an Ordinary Annuity\r\n\r\nwhere;\r\nP : Present value of all payments\r\nA : Periodic payment\r\nr : Interest rate per period\r\nn : Number of periods (peyments)\r\nCalculate P, given A, r and n. Round to the nearest cent. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 230.377px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.997px 115.188px; transform-origin: 406.997px 115.188px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eTheorem : Present Value of an Ordinary Annuity\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 37.6379px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 18.8189px; text-align: left; transform-origin: 383.996px 18.8189px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-16px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"116\" height=\"37.5\" style=\"width: 116px; height: 37.5px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ewhere;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7555px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 390.993px 40.8778px; transform-origin: 390.998px 40.8778px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eP : Present value of all payments\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eA : Periodic payment\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003er : Interest rate per period\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003en : Number of periods (peyments)\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eCalculate P, given A, r and n. Round to the nearest cent. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function P = annuityPresent(A,r,n)\r\n\r\nend","test_suite":"%%\r\nA = 100;\r\nr = 0.004;\r\nn = 160;\r\nP = 11800.85\r\nassert(abs(annuityPresent(A,r,n) - P ) \u003c= 1e-2)\r\n\r\n%%\r\nA = 1500;\r\nr = 0.01;\r\nn = 24;\r\nP = 31865.08;\r\nassert(abs(annuityPresent(A,r,n) - P) \u003c= 1e-2)\r\n\r\n\r\n%%\r\nA = 1;\r\nr = 0.001;\r\nn = 100;\r\nP = 95.12;\r\nassert(abs(annuityPresent(A,r,n) - P) \u003c= 1e-2)","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":8703,"edited_by":8703,"edited_at":"2022-10-01T16:34:56.000Z","deleted_by":null,"deleted_at":null,"solvers_count":35,"test_suite_updated_at":"2022-10-01T16:34:56.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-09-30T07:57:13.000Z","updated_at":"2026-02-18T09:20:29.000Z","published_at":"2022-09-30T16:54:32.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTheorem : Present Value of an Ordinary Annuity\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eP = A \\\\frac{(1+r)^n-1}{r (1+r)^n}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eP : Present value of all payments\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA : Periodic payment\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003er : Interest rate per period\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003en : Number of periods (peyments)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate P, given A, r and n. Round to the nearest cent. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":56120,"title":"Compound Interest : Compounding Periods","description":"Theorem : Compound Interest\r\n\r\nwhere,\r\nF : Future value at the end of n periods\r\nP : Present value\r\nr : Annual nominal rate\r\nn : Total number of compounding periods\r\nCalculate n, given F, P and r. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 213.741px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.997px 106.87px; transform-origin: 406.997px 106.87px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eTheorem : Compound Interest\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"89\" height=\"19.5\" style=\"width: 89px; height: 19.5px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ewhere,\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7555px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 390.993px 40.8778px; transform-origin: 390.998px 40.8778px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eF : Future value at the end of n periods\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eP : Present value\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003er : Annual nominal rate\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003en : Total number of compounding periods\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eCalculate n, given F, P and r. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function n = compoundMaturity(F,P,r)\r\n\r\nend","test_suite":"%%\r\nF = 100;\r\nP = 50;\r\nr = 0.05;\r\nn = 14.21;\r\nassert(abs(compoundMaturity(F,P,r) - n ) \u003c= 1e-2)\r\n\r\n%%\r\nF = 1467;\r\nP = 467;\r\nr = 0.0123;\r\nn = 93.63;\r\nassert(abs(compoundMaturity(F,P,r) - n )\u003c= 1e-2)\r\n\r\n\r\n%%\r\nF = 1500;\r\nP = 380;\r\nr = 0.0567;\r\nn = 24.90;\r\nassert(abs(compoundMaturity(F,P,r) - n) \u003c= 1e-2)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":8703,"edited_by":8703,"edited_at":"2022-10-01T16:27:13.000Z","deleted_by":null,"deleted_at":null,"solvers_count":31,"test_suite_updated_at":"2022-10-01T16:27:13.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-09-30T05:22:51.000Z","updated_at":"2026-02-16T16:24:46.000Z","published_at":"2022-09-30T16:55:48.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTheorem : Compound Interest\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eF = P(1+r)^n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eF : Future value at the end of n periods\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eP : Present value\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003er : Annual nominal rate\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003en : Total number of compounding periods\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate n, given F, P and r. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":56080,"title":"Simple Interest : Calculate Present Value","description":"Theorem : Simple Interest\r\n\r\nwhere;\r\nF : Future Value\r\nP : Present Value\r\nr : Annual simple interest rate (decimal)\r\nt : Time in years\r\nCalculate P, given F, r and t. Round to nearest cent.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 213.741px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.997px 106.87px; transform-origin: 406.997px 106.87px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eTheorem : Simple Interest\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"88\" height=\"18.5\" style=\"width: 88px; height: 18.5px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ewhere;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7555px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 390.993px 40.8778px; transform-origin: 390.998px 40.8778px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eF : Future Value\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eP : Present Value\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003er : Annual simple interest rate (decimal)\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003et : Time in years\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eCalculate P, given F, r and t. Round to nearest cent.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function P = simplePresent(F,r,t)\r\n\r\nend","test_suite":"%%\r\nF = 100;\r\nr = 0.045;\r\nt = 4;\r\ny_correct = 84.75;\r\nassert(abs(simplePresent(F,r,t)-y_correct)\u003c=1e-2)\r\n\r\n%%\r\nF = 48;\r\nr = 0.11;\r\nt = 90;\r\ny_correct = 4.40;\r\nassert(abs(simplePresent(F,r,t)-y_correct)\u003c=1e-2)\r\n\r\n\r\n%%\r\nF = 140000;\r\nr = 0.04;\r\nt = 7;\r\ny_correct = 109375;\r\nassert(abs(simplePresent(F,r,t)-y_correct)\u003c=1e-2)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":8703,"edited_by":8703,"edited_at":"2022-10-01T16:19:38.000Z","deleted_by":null,"deleted_at":null,"solvers_count":48,"test_suite_updated_at":"2022-10-01T16:19:38.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-09-29T18:31:37.000Z","updated_at":"2026-02-16T12:18:29.000Z","published_at":"2022-09-30T16:57:26.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTheorem : Simple Interest\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eF = P(1+rt)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eF : Future Value\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eP : Present Value\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003er : Annual simple interest rate (decimal)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003et : Time in years\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate P, given F, r and t. Round to nearest cent.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":56085,"title":"Simple Interest : Calculate annual simple interest rate","description":"Theorem : Simple Interest\r\n\r\nwhere;\r\nF : Future Value\r\nP : Present Value\r\nr : Annual simple interest rate (decimal)\r\nt : Time in years\r\nCalculate r, given F, P and t.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 213.741px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.997px 106.87px; transform-origin: 406.997px 106.87px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eTheorem : Simple Interest\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"88\" height=\"18.5\" style=\"width: 88px; height: 18.5px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ewhere;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7555px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 390.993px 40.8778px; transform-origin: 390.998px 40.8778px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eF : Future Value\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eP : Present Value\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003er : Annual simple interest rate (decimal)\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003et : Time in years\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eCalculate r, given F, P and t.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function r = simpleRate(F,P,t)\r\n\r\nend","test_suite":"%%\r\nF = 500;\r\nP = 100;\r\nt = 6;\r\nr = 0.6667;\r\nassert(abs(simpleRate(F,P,t)-r) \u003c= 1e-2)\r\n\r\n%%\r\nF = 360000;\r\nP = 300000;\r\nt = 15;\r\nr = 0.0133;\r\nassert(abs(simpleRate(F,P,t)-r )\u003c= 1e-2)\r\n\r\n\r\n%%\r\nF = 2250;\r\nP = 1000;\r\nt = 7;\r\nr = 0.1786;\r\nassert(abs(simpleRate(F,P,t)-r) \u003c= 1e-2)","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":8703,"edited_by":8703,"edited_at":"2022-10-01T16:20:49.000Z","deleted_by":null,"deleted_at":null,"solvers_count":44,"test_suite_updated_at":"2022-10-01T16:20:49.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-09-29T18:44:04.000Z","updated_at":"2026-02-16T12:16:52.000Z","published_at":"2022-09-30T16:57:09.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTheorem : Simple Interest\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eF = P(1+rt)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eF : Future Value\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eP : Present Value\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003er : Annual simple interest rate (decimal)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003et : Time in years\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate r, given F, P and t.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":56125,"title":"Ordinary Annuity : Future Value","description":"Theorem : Future Value of an Ordinary Annuity \r\n\r\nwhere;\r\nF : Future value\r\nA : Periodic payment\r\nr : Rate per period\r\nn : Number of periods (payments)\r\nCalculate F, given, A, r and n. Round to the nearest cent.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 229.056px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.997px 114.522px; transform-origin: 406.997px 114.528px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eTheorem : Future Value of an Ordinary Annuity \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 36.3166px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 18.1526px; text-align: left; transform-origin: 383.996px 18.1583px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"117.5\" height=\"36.5\" style=\"width: 117.5px; height: 36.5px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ewhere;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7555px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 390.993px 40.8778px; transform-origin: 390.998px 40.8778px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eF : Future value\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eA : Periodic payment\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003er : Rate per period\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003en : Number of periods (payments)\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eCalculate F, given, A, r and n. Round to the nearest cent.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function F = annuityFuture(A,r,n)\r\n\r\nend","test_suite":"%%\r\nA = 150;\r\nr = 0.055;\r\nn = 15;\r\nF = 3361.30;\r\nassert(abs(annuityFuture(A,r,n) - F) \u003c= 1e-2)\r\n\r\n%%\r\nA = 4000;\r\nr = 0.017;\r\nn = 55;\r\nF = 359358.70;\r\nassert(abs(annuityFuture(A,r,n) - F) \u003c= 1e-2)\r\n\r\n\r\n%%\r\nA = 120;\r\nr = 0.041;\r\nn = 4;\r\nF = 510.34;\r\nassert(abs(annuityFuture(A,r,n) - F )\u003c= 1e-2)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":8703,"edited_by":8703,"edited_at":"2022-10-01T16:37:51.000Z","deleted_by":null,"deleted_at":null,"solvers_count":48,"test_suite_updated_at":"2022-10-01T16:37:51.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-09-30T05:37:05.000Z","updated_at":"2026-02-17T08:42:39.000Z","published_at":"2022-09-30T16:55:31.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTheorem : Future Value of an Ordinary Annuity \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eF = A \\\\frac{(1+r)^n -1}{r}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eF : Future value\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA : Periodic payment\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003er : Rate per period\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003en : Number of periods (payments)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate F, given, A, r and n. Round to the nearest cent.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":56130,"title":"Ordinary Annuity : Periodic Payments (Future Value)","description":"Theorem : Future Value of an Ordinary Annuity \r\n\r\nwhere;\r\nF : Future value\r\nA : Periodic payment\r\nr : Rate per period\r\nn : Number of periods (payments)\r\nCalculate A, given, F, r and n. Round to the nearest cent.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 229.056px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.997px 114.522px; transform-origin: 406.997px 114.528px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eTheorem : Future Value of an Ordinary Annuity \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 36.3166px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 18.1526px; text-align: left; transform-origin: 383.996px 18.1583px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"117.5\" height=\"36.5\" style=\"width: 117.5px; height: 36.5px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ewhere;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7555px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 390.993px 40.8778px; transform-origin: 390.998px 40.8778px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eF : Future value\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eA : Periodic payment\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003er : Rate per period\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003en : Number of periods (payments)\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eCalculate A, given, F, r and n. Round to the nearest cent.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function A = annuityFPayment(F,r,n)\r\n\r\nend","test_suite":"%%\r\nF = 5000;\r\nr = 0.02;\r\nn = 9;\r\nA = 512.58;\r\nassert(abs(annuityFPayment(F,r,n) - A) \u003c= 1e-2)\r\n\r\n%%\r\nF = 1457.85;\r\nr = 0.07;\r\nn = 15;\r\nA = 58.01;\r\nassert(abs(annuityFPayment(F,r,n) - A) \u003c= 1e-2)\r\n\r\n\r\n%%\r\nF = 1e6;\r\nr = 0.1;\r\nn = 30;\r\nA = 6079.25;\r\nassert(abs(annuityFPayment(F,r,n) - A) \u003c= 1e-2)","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":8703,"edited_by":8703,"edited_at":"2022-10-01T16:29:58.000Z","deleted_by":null,"deleted_at":null,"solvers_count":47,"test_suite_updated_at":"2022-10-01T16:29:58.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-09-30T05:43:13.000Z","updated_at":"2026-02-18T09:27:30.000Z","published_at":"2022-09-30T16:55:14.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTheorem : Future Value of an Ordinary Annuity \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eF = A \\\\frac{(1+r)^n -1}{r}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eF : Future value\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA : Periodic payment\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003er : Rate per period\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003en : Number of periods (payments)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate A, given, F, r and n. Round to the nearest cent.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":56105,"title":"Compound Interest: Interest Rate","description":"Theorem : Compound Interest\r\n\r\nwhere,\r\nF : Future value at the end of n periods\r\nP : Present value\r\nr : Annual nominal rate\r\nn : Total number of compounding periods\r\nCalculate r, given F, P and n. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 213.741px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.997px 106.87px; transform-origin: 406.997px 106.87px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eTheorem : Compound Interest\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"89\" height=\"19.5\" style=\"width: 89px; height: 19.5px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ewhere,\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7555px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 390.993px 40.8778px; transform-origin: 390.998px 40.8778px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eF : Future value at the end of n periods\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eP : Present value\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003er : Annual nominal rate\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003en : Total number of compounding periods\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eCalculate r, given F, P and n. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function r = compoundRate(F,P,n)\r\n\r\nend","test_suite":"%%\r\nF = 500;\r\nP = 100;\r\nn = 10;\r\nr = 0.1746;\r\nassert(abs(compoundRate(F,P,n)-r) \u003c= 1e-2)\r\n\r\n%%\r\nF = 10000;\r\nP = 9000;\r\nn = 2;\r\nr = 0.054;\r\nassert(abs(compoundRate(F,P,n)-r )\u003c= 1e-2)\r\n\r\n\r\n%%\r\nF = 320;\r\nP = 40;\r\nn = 75;\r\nr = 0.0281;\r\nassert(abs(compoundRate(F,P,n)-r )\u003c= 1e-2)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":8703,"edited_by":8703,"edited_at":"2022-10-01T16:26:10.000Z","deleted_by":null,"deleted_at":null,"solvers_count":60,"test_suite_updated_at":"2022-10-01T16:26:10.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-09-30T05:20:21.000Z","updated_at":"2026-02-16T16:39:39.000Z","published_at":"2022-09-30T16:56:03.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTheorem : Compound Interest\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eF = P(1+r)^n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eF : Future value at the end of n periods\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eP : Present value\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003er : Annual nominal rate\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003en : Total number of compounding periods\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate r, given F, P and n. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":56140,"title":"Ordinary Annuity : Number of payments (Future Value)","description":"Theorem : Future Value of an Ordinary Annuity \r\n\r\nwhere;\r\nF : Future value\r\nA : Periodic payment\r\nr : Rate per period\r\nn : Number of periods (payments)\r\nCalculate n, given, F, A and r. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 229.056px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.997px 114.522px; transform-origin: 406.997px 114.528px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eTheorem : Future Value of an Ordinary Annuity \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 36.3166px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 18.1526px; text-align: left; transform-origin: 383.996px 18.1583px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"117.5\" height=\"36.5\" style=\"width: 117.5px; height: 36.5px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ewhere;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7555px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 390.993px 40.8778px; transform-origin: 390.998px 40.8778px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eF : Future value\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eA : Periodic payment\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003er : Rate per period\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003en : Number of periods (payments)\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eCalculate n, given, F, A and r. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function n = annuityFMaturity(F,A,r)\r\n\r\nend","test_suite":"%%\r\nF = 500000;\r\nA = 10000;\r\nr = 0.085\r\nn = 20.33;\r\nassert(abs(annuityFMaturity(F,A,r) - n) \u003c= 1e-2)\r\n\r\n%%\r\nF = 100;\r\nA = 1;\r\nr = 0.074\r\nn = 29.81;\r\nassert(abs(annuityFMaturity(F,A,r) - n) \u003c= 1e-2)\r\n\r\n\r\n%%\r\nF = 1000;\r\nA = 0.1;\r\nr = 0.052\r\nn = 123.40;\r\nassert(abs(annuityFMaturity(F,A,r) - n )\u003c= 1e-2)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":8703,"edited_by":8703,"edited_at":"2022-10-01T16:30:39.000Z","deleted_by":null,"deleted_at":null,"solvers_count":30,"test_suite_updated_at":"2022-10-01T16:30:39.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-09-30T07:39:23.000Z","updated_at":"2026-02-17T09:03:03.000Z","published_at":"2022-09-30T16:54:47.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTheorem : Future Value of an Ordinary Annuity \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eF = A \\\\frac{(1+r)^n -1}{r}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eF : Future value\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA : Periodic payment\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003er : Rate per period\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003en : Number of periods (payments)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate n, given, F, A and r. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":56165,"title":"Ordinary Annuity : Number of Payments (Present Value)","description":"Theorem : Present Value of an Ordinary Annuity\r\n\r\nwhere;\r\nP : Present value of all payments\r\nA : Periodic payment\r\nr : Interest rate per period\r\nn : Number of periods (peyments)\r\nCalculate n, given P, A and r. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 230.733px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 115.367px; transform-origin: 407px 115.367px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 151.5px 8px; transform-origin: 151.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eTheorem : Present Value of an Ordinary Annuity\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 38px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 19px; text-align: left; transform-origin: 384px 19px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-16px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 116px; height: 38px;\" width=\"116\" height=\"38\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21px 8px; transform-origin: 21px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7333px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 391px 40.8667px; transform-origin: 391px 40.8667px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 103.5px 8px; transform-origin: 103.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eP : Present value of all payments\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 65px 8px; transform-origin: 65px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA : Periodic payment\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 81px 8px; transform-origin: 81px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003er : Interest rate per period\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 105.5px 8px; transform-origin: 105.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003en : Number of periods (peyments)\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 92.5px 8px; transform-origin: 92.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCalculate n, given P, A and r. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function n = annuityPMaturity(P,A,r)\r\n \r\nend","test_suite":"%%\r\nP = 1200;\r\nA = 500;\r\nr = 0.05;\r\nn = 2.62;\r\nassert(abs(annuityPMaturity(P,A,r) - n )\u003c= 1e-2)\r\n\r\n%%\r\nP = 10000;\r\nA = 1500;\r\nr = 0.0075;\r\nn = 6.86;\r\nassert(abs(annuityPMaturity(P,A,r) - n) \u003c= 1e-2)\r\n\r\n\r\n%%\r\nP = 400;\r\nA = 20;\r\nr = 0.0025;\r\nn = 20.54;\r\nassert(abs(annuityPMaturity(P,A,r) - n) \u003c= 1e-2)\r\n\r\n%%\r\nP = randi(10)*1e3;\r\nA = 2*P;\r\nr = 1;\r\nn = 1;\r\nassert(abs(annuityPMaturity(P,A,r) - n) \u003c= 1e-2)\r\n\r\n%%\r\nP = randi(10)*3e3;\r\nA = 4*P/3;\r\nr = 1;\r\nn = 2;\r\nassert(abs(annuityPMaturity(P,A,r) - n) \u003c= 1e-2)","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":8703,"edited_by":223089,"edited_at":"2022-12-19T07:56:40.000Z","deleted_by":null,"deleted_at":null,"solvers_count":22,"test_suite_updated_at":"2022-12-19T07:56:40.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-09-30T16:36:30.000Z","updated_at":"2026-02-18T10:17:09.000Z","published_at":"2022-09-30T16:53:13.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTheorem : Present Value of an Ordinary Annuity\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eP = A \\\\frac{(1+r)^n-1}{r (1+r)^n}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eP : Present value of all payments\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA : Periodic payment\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003er : Interest rate per period\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003en : Number of periods (peyments)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate n, given P, A and r. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":56160,"title":"Ordinary Annuity : Rate (Present Value)","description":"Theorem : Present Value of an Ordinary Annuity\r\n\r\nwhere;\r\nP : Present value of all payments\r\nA : Periodic payment\r\nr : Interest rate per period\r\nn : Number of periods (peyments)\r\nCalculate r, given P, A and n. Assume interest rate is in [0, 1].","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 230.377px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.997px 115.188px; transform-origin: 406.997px 115.188px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eTheorem : Present Value of an Ordinary Annuity\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 37.6379px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 18.8189px; text-align: left; transform-origin: 383.996px 18.8189px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-16px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"116\" height=\"37.5\" style=\"width: 116px; height: 37.5px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ewhere;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7555px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 390.993px 40.8778px; transform-origin: 390.998px 40.8778px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eP : Present value of all payments\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eA : Periodic payment\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003er : Interest rate per period\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003en : Number of periods (peyments)\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eCalculate r, given P, A and n. Assume interest rate is in [0, 1].\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function r = annuityPRate(P,A,n)\r\n\r\nend","test_suite":"%%\r\nP = 650000;\r\nA = 65000;\r\nn = 25;\r\nr =0.0878;\r\nassert(abs(annuityPRate(P,A,n) - r )\u003c= 1e-4)\r\n\r\n\r\n%%\r\nP = 10000;\r\nA = 1000;\r\nn = 12;\r\nr =0.0292;\r\nassert(abs(annuityPRate(P,A,n) - r) \u003c= 1e-4)\r\n\r\n%%\r\nP = 50000;\r\nA = 250;\r\nn = 360;\r\nr =0.0037;\r\nassert(abs(annuityPRate(P,A,n) - r) \u003c= 1e-4)\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":8703,"edited_by":8703,"edited_at":"2022-10-01T16:33:28.000Z","deleted_by":null,"deleted_at":null,"solvers_count":14,"test_suite_updated_at":"2022-10-01T16:33:28.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-09-30T15:59:26.000Z","updated_at":"2022-10-01T16:33:34.000Z","published_at":"2022-09-30T16:53:23.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTheorem : Present Value of an Ordinary Annuity\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eP = A \\\\frac{(1+r)^n-1}{r (1+r)^n}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eP : Present value of all payments\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA : Periodic payment\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003er : Interest rate per period\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003en : Number of periods (peyments)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate r, given P, A and n. Assume interest rate is in [0, 1].\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":56135,"title":"Ordinary Annuity : Rate (Future Value)","description":"Theorem : Future Value of an Ordinary Annuity \r\n\r\nwhere;\r\nF : Future value\r\nA : Periodic payment\r\nr : Rate per period\r\nn : Number of periods (payments)\r\nCalculate r, given, F, A and n. Assume interest rate is a positive real number. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 229.233px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 114.617px; transform-origin: 407px 114.617px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 150px 8px; transform-origin: 150px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eTheorem : Future Value of an Ordinary Annuity \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 36.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 18.25px; text-align: left; transform-origin: 384px 18.25px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 117.5px; height: 36.5px;\" width=\"117.5\" height=\"36.5\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21px 8px; transform-origin: 21px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7333px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 391px 40.8667px; transform-origin: 391px 40.8667px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 50.5px 8px; transform-origin: 50.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eF : Future value\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 65px 8px; transform-origin: 65px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA : Periodic payment\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 58px 8px; transform-origin: 58px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003er : Rate per period\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 105.5px 8px; transform-origin: 105.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003en : Number of periods (payments)\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 242px 8px; transform-origin: 242px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCalculate r, given, F, A and n. Assume interest rate is a positive real number. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function r = annuityFRate(F,A,n)\r\n \r\nend","test_suite":"%%\r\nfiletext = fileread('annuityFRate.m');\r\nillegal = contains(filetext, 'switch') || contains(filetext, 'if')\r\nassert(~illegal)\r\n\r\n%%\r\nF = 500000;\r\nA = 1000;\r\nn = 45;\r\nr = 0.0884;\r\nassert(abs(annuityFRate(F,A,n) - r) \u003c= 1e-4)\r\n\r\n%%\r\nF = 60000;\r\nA = 1500;\r\nn = 20;\r\nr = 0.0677;\r\nassert(abs(annuityFRate(F,A,n) - r) \u003c= 1e-4)\r\n\r\n\r\n%%\r\nF = 125000;\r\nA = 400;\r\nn = 120;\r\nr = 0.0142;\r\nassert(abs(annuityFRate(F,A,n) - r )\u003c= 1e-4)\r\n\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":5,"created_by":8703,"edited_by":223089,"edited_at":"2022-12-12T06:15:30.000Z","deleted_by":null,"deleted_at":null,"solvers_count":17,"test_suite_updated_at":"2022-12-12T06:15:30.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-09-30T05:52:00.000Z","updated_at":"2022-12-12T06:15:31.000Z","published_at":"2022-09-30T16:55:04.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTheorem : Future Value of an Ordinary Annuity \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eF = A \\\\frac{(1+r)^n -1}{r}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eF : Future value\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA : Periodic payment\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003er : Rate per period\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003en : Number of periods (payments)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate r, given, F, A and n. Assume interest rate is a positive real number. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":56150,"title":"Ordinary Annuity : Periodic Payment (Present Value)","description":"Theorem : Present Value of an Ordinary Annuity\r\n\r\nwhere;\r\nP : Present value of all payments\r\nA : Periodic payment\r\nr : Interest rate per period\r\nn : Number of periods (peyments)\r\nCalculate A, given P, r and n. Round to the nearest cent. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 230.377px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.997px 115.188px; transform-origin: 406.997px 115.188px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eTheorem : Present Value of an Ordinary Annuity\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 37.6379px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 18.8189px; text-align: left; transform-origin: 383.996px 18.8189px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-16px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAOgAAABLCAYAAAB6Ics4AAAAAXNSR0IArs4c6QAADrdJREFUeF7tnQfMNkURx/+o0Sj23qJCbBFsMUHUWGONsWAUewE1CirYsHcBUVGDCljA2HuJXSyxGyUWFLsSbChYo0ZQseVHZpL1vmt7z91ze+/NJl++5H3ubmdn9787O3U3RQsOBAeK5cBuxVIWhAUHggMKgMYiCA4UzIEAaMGTE6QFBwKgsQaCAwVzIABa8OQEacGBAOg8a+DSkm4s6bOS/jMPCUX0ej5Jt5X0LUl/LIKiwogIgG5/Qq4l6XGSjpB01va7L67Hq0h6kqRjJP28OOpmJigAut0JuI6kJ0p6Tk9wXkbSgZIuaIDeLrXb6+0Kkp66IpBezTbpb0p6RxubA6DbW4SXswX4Wkmf7+gWYD7MJvHqBugXbo/UWXq6haT7SXqapL/NQsH0nQLMgyU9UhLXnAdJelsAdHrGd/Vwfjs5LyTpKEn/aniB3x8qiRPlApKeIOliKwEoPHqKpLMlvVLSfys84vebSbqV/f8LSc+UdBdJTzcp44GSvtE1GTP8fklJj5DEnfuqtvFCRgB0hsmo63IvSa+SdJCkH7XQxCKk/VsSJ+7bJd1+QoDeRNKRkk42EfrvM/NrD0nH2530ew20PETSm0zC4BT6qaTLSzrBQHDizGOo657NFmUg/64r6d2Srh8ALWOmAN1z7UR8toGvD2WIuYg/d5oQoIiVX5KE2M1pfU4fwiZ8Bl4hyiNhPL+GV1zJODX3l/QpSV+U9EFJj7fND/B+dUL6xvg0eoh3SbphAHQMdm7+De6QnITPs0XV94trBCi8uYOB9P6STq8w6xJ2Ut5b0uF2+vPIKyRdye52v+3L4JmeC4DOxPimbu9uJyAKEMSxvm2tAL2mpHdKeoGkD1WYdQNJ75V0pqQDJJ0myTfAz5mk0nS/78v3qZ8LgE7N4Yzvu8iG7RMlwZ8z3l0iQC8saW9JjPdGkvaVdJKddJc1URRgYVrA1FSnrfVTkjsoYm6qLEIJ9FZJj5X0GhOBURqhFb+XpA9k8HeuRwOgc3G+pl80sMdK+r2ZD/6ZQdsSAYq9FoABFgBEu6OkHxsf7mp/+7ak+zYozPgGmm4A/RhJf7V3/O93NnPMd6TzorG4O3P35Hu8g21x7rt02zQHQDNAMPWjron9gt2rcvpbIkB9fJycn5R0qoEM5ww0r9wTj5P0FjOpNNk7UaZxMj5A0u/so4CP9/4g6RBzDfTT9lxJHzZFHKdzyWJuADQHBRM/65OB6QBNaU5bMkBdFEVbyT3xZ6bcqdo2m/iBXZMTMT1lMQkBwhdLerWJt4jULzEgP0PSmws/PRlvADQHBRM/65Px0i6PkRo6xgBouhg2GSr3xb6eTC6KInoSDIBi7MmS/pJBAAA/rEUMzvjULo+mfB36nU3MUgHQoVyf4L01AvTKthndRtJv7L6IiJ/TAqDGrS5fXC71d5N0H/MdrGMynjGEC2EwRgTZSX6UeICgSYRPOU4Gzqc1irg4P3zcXBRx2cN97x856DRe38PAnWOayuxmlscnOUHdvYoRoYF7sCkAdpe0n6RnmWz9ZbvAo0nbCQ1FBTa5T1c0in3HtkYlEaLty037ytr4TF9mJc+xGQJ0TlKUQjupTQLQRyVqc7w2iDhITQao1d9nXMS4jLd+6R4dXZN+cfOfZXPCCM5i+XXXS5Xf12Zm8fGygWOTfLikP2XyDMUPawwb8qHmPJ/5iaIfHx2g6aWfkdd54Ls3x82NNbeWlHvvKI2rromErp9Iwr0M21tOc99R/C7X4KiQLr5HD9Bcw9tLmTkFaexFOcxeyLOjA9TtTxiImxZqVTPWGUZTODOJ8n+jJFzLiJSgYXDHQTu34VuKFrfJMN/0vTG0uF20ju0sj1sjuoihGxr0wnOuFWSdGCIed4157t9HB6jbnzAyf9Tun1WxpQrQoYt5bubRv8clIhXgAfMyI2roiQDfsM9hC31/xgDJWYQdEbe5ocqWru7GBKi7NWLDxF82V2JwWpFcCFbnaoEWeKc14lc/ZoMi1QvifKN9uEuLy3fS+yciR502M90V2ty4lsBsdnAM4fh7EjiNRwytaexdY3J3NADfpdH0oGS050Rz8A4NdzfAil0R0W+s3D1jAjSVtPAcYuHlNpSO8P6UhqDt3O+V8jyB+LeThGY6tYiQKA1JjZA/QudwCf2/1gVQv7ADUhodVCMM+Aa75evsGU4cYvZyVeslMNPHCwDwUOH08uBa3MxS39Aceq9h9zH48vWcFyd+trSA7X3MrMV6OmPisS/i810ATZU/dScj75M28Q222yMCIwr+qufoOY0JK9qkjXliI5rjMoaIhXtamtVgqCaXscEnTkTEVkxSS9y8NpmjPu+yOWKeITKFO2g0WzhtjEDB4SLeR8zGicsWuVWubYZkcuigXueexeL7ZQZnSwIoyqDXS3qPecJwL7iIJfpiR99E8QFLWID4kX4lFuAuKyQ2sAbQtJ2gbiJwH0y8hViw3DdpeBDh5fE1s3l9f8FJmF1MZ0NCnHclGH8nXQn/aJsqv8ihQ3pJxOXvZmxkO/1RRG1s6YSZeXjZTh9zr/G1ATRNLzHG4uxF0EwPsemQ/wfx1iUGJyX1ohqqyU2HBUjR3qHRLTED3banAHBinjk6wLkr69sA6uklUJQglhGbN5b2cNuLoK0/97cFnF1tqCa3+l20ephf4GffEKwu2pb4O1rrPSWRQjPu5TUz2AbQ1JNmk/Ca0hcO/rYoJ7hL16V6TNMkbmLfK50PQV+BHGgCaNW9bwzRrm74cyuJ3N/2h2ZWIR9ttaXhUztZkihweQZJTQCtxvQRcjbFfWlugJJpj2BipIWmhNKpAzieLV28ICsdGdCjBQeGcgCfb8yH59nn6loa0/cJc+/bxcthaO+FvIe/LdpU/GtxSqg7PSG1Kk3UOWukQwKgmGSiBQeGcoCMiK0A9Zg+OhhLMTKU2Cne81ophMX1iVJJT/ouNzYASoqQaMGBoRzAG68RoFe0BE+eIpGMAtX8pEM7LuU9wuHIMsdJl2aOq6MvdQLnd8wxuPzl5LgtZdxBx8I4kIq4eLpwF+NEoR6INxx68a7h39LDfy5qeVSp5YE9ksa4ACuifCrmYgrBsRkwEyrGXdRb0zsLm/4gt3QOdPnilk5/0Bcc2NEcCIDu6OmNwS2dAwHQpc9gPv1cZW5pKWnmrgeaT/14bxDwQSQWPuZc44psAdAip2UyogifI+KIuik/mKyX5XwYUxt+0ceU6sYaAF3OYtqUUrJDUKOU9Cl9wEkamwPNDnzEpp0X/D58IcKoSJAGQAteOSOS5rGoVJ+muFCbgz7AJGCdpF0E7OeUfRiR5K1+CsccvMpIJ1uXeN1T0eC3jZcYzv1kxyC/EDmYcGbBAjK6t10AdKvrYLbOWHyUYkCca8r8j1mJgAFOFCJ8cFbBtLQGgHqiuLM7ciF56CEbGGY64qEJ9D/B0v6cOPYMB0DH5mh53yOsjUwRuDO25SpmkdKwBaepXqYCaGn5kPawzItsYnVRTZ7AYH9zDyXJFylGsakfZFkIkVBGbQHQUdlZ5MfI7o6zRU7CsyXm5N2U+e4xRm1RPOeqvtlpAoPDrWo4fZK9kE1wkmoKAdBNp7Xs931RUVsmpz7pGgHKTJLyhhQ/JHg7vTK1nsDgTEkHWN1TT6pHQjnS4oxeODgAWjbANqUOMZKaOdxBc8SvtQKUQAcyCpJpsppe1hMYkC8ZMxUnLEojshCST4laNKO3AOjoLB39gxjUSTvD4qHGy00tORsiFQm2WBxoEilWhRibxrWSAA3FRm66miUCFE313sYrwrX2lXSSiaIk1eauyMmHFpt7dZ2yzCUO7qBpgIiHHFL+hM2OeE1PSA5/8dWmD6r6nTPmCgiAjsnNab4FQFk415N0rIGUEMAjTSuLbdNbWhPH71SAO7cMwxIBCojgExsWJxyNLIyU74BvHp3VlkfZgQjY0ju7Z82nFOIh5nnkYD7X6uKi+Qb8o4q5AdBpQDXFV73qFwvtnpLIVk8aVIrl+oLkhHAnBM/piyiGySRnZ18iQJ3nnJxkZjzVQEb8LtFKKHKOsyB9SnA0mZuI/UV0TcMQvT4ReY0pTQFPObHRjPMcCefIC53D415rJADai01FPOT1bwAeJ8Jelq6FROJ1zUGG2JVbHXzJAPW7IrVsTrMKAdgp+2ZP5LqAyJpbjW6SRRIAnYStk3zUS/shop0l6bCOeqUOMootefLxvoSNAdC0oFbffuuey7HDpulpKDSFIwE5p5o2sbr+ADi8DYBuMmsre7ea1QGRqi2PEuxZI0Crye5Q6OQWkg6ArgxcYww3Le1HqY06O121nzWKuGmyu6E1VbkOkBgOcHMCz9pCxJ2V/b07T4soI67WebpUP7ZGJZEnu8P8tN/AFD0AFKBzkqK1nbUFQGdlf+/OvYgyeXnR4J7c4821mVnS/MU4DeDiWK0E38U2rw8L7w6VhPP8rC0AOiv7e3WeFlHOLSLMKXDwShwVUqXU0EoIbspCsYatefYWAJ19CjoJSIso5y48/EdxXcPriEXXt42hxe3qCzGS0u9j1f1xLfcmdVydX8TCFpHBMgDatYzm/92LKPcpO1GldnczrGO0J+qiry2QSuDYEfFCGqps6eLcmABNtdybFLhC4iDWE/c9+D17C4DOPgWtBHgMIoqhoQsP1zdcALvuZJ41AE8ltMSc3DQULoAVuyKn8FglKMcEaKrl7sr838Rw38xO6Qja3uqKCYBuld2zdMa96njzEyXAuJRWWsD2PqYdx2/5jFKYFAAtZSampYOAbU5QNJO5ms1pKSvj6yjiqBFL6Bh39mJaALSYqZiUEC8WRScsxKZKbpMSUejHwQAiPfduUpIWVek7AFroqpmALE4JYiLxROI+2VdhNAEpRX0SUZt7+lF23y6KuABoUdMxOTGAFBMCAccEM68dpIAT88zRJYKT1RAAnRwTxXVAADixpOR2HTW4uLiRthOE2L+n8aEosTYlOwC6sFUV5K6LAwHQdc13jHZhHAiALmzCgtx1cSAAuq75jtEujAP/A6Q/i3kudrgvAAAAAElFTkSuQmCC\" width=\"116\" height=\"37.5\" style=\"width: 116px; height: 37.5px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ewhere;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7555px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 390.993px 40.8778px; transform-origin: 390.998px 40.8778px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eP : Present value of all payments\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eA : Periodic payment\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003er : Interest rate per period\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003en : Number of periods (peyments)\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eCalculate A, given P, r and n. Round to the nearest cent. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function A = annuityPPayment(P,r,n)\r\n\r\nend","test_suite":"%%\r\nP = 1500;\r\nr = 0.07;\r\nn = 20;\r\nA = 141.59;\r\nassert(abs(annuityPPayment(P,r,n) - A )\u003c= 1e-2)\r\n\r\n%%\r\nP = 1e6;\r\nr = 0.005;\r\nn = 240;\r\nA = 7164.31;\r\nassert(abs(annuityPPayment(P,r,n) - A )\u003c= 1e-2)\r\n\r\n%%\r\nP = 50000;\r\nr = 0.1;\r\nn = 3;\r\nA = 20105.74;\r\nassert(abs(annuityPPayment(P,r,n) - A )\u003c= 1e-2)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":8703,"edited_by":8703,"edited_at":"2022-10-01T16:32:47.000Z","deleted_by":null,"deleted_at":null,"solvers_count":36,"test_suite_updated_at":"2022-10-01T16:32:47.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-09-30T08:07:42.000Z","updated_at":"2026-02-09T13:35:50.000Z","published_at":"2022-09-30T16:53:42.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTheorem : Present Value of an Ordinary Annuity\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eP = A \\\\frac{(1+r)^n-1}{r (1+r)^n}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eP : Present value of all payments\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA : Periodic payment\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003er : Interest rate per period\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003en : Number of periods (peyments)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate A, given P, r and n. Round to the nearest cent. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":56100,"title":"Compound Interest: Present Value","description":"Theorem : Compound Interest\r\n\r\nwhere,\r\nF : Future value at the end of n periods\r\nP : Present value\r\nr : Annual nominal rate\r\nn : Total number of compounding periods\r\nCalculate P, given F, r and n. Round to the nearest cent.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 213.741px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.997px 106.87px; transform-origin: 406.997px 106.87px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eTheorem : Compound Interest\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"89\" height=\"19.5\" style=\"width: 89px; height: 19.5px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ewhere,\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7555px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 390.993px 40.8778px; transform-origin: 390.998px 40.8778px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eF : Future value at the end of n periods\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eP : Present value\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003er : Annual nominal rate\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003en : Total number of compounding periods\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eCalculate P, given F, r and n. Round to the nearest cent.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function P = compoundPresent(F,r,n)\r\n\r\nend","test_suite":"%%\r\nF = 100;\r\nr = 0.07;\r\nn = 5;\r\nP = 71.30;\r\nassert(abs(compoundPresent(F,r,n)-P)\u003c=1e-2)\r\n\r\n%%\r\nF = 200;\r\nr = 0.045;\r\nn = 14;\r\nP = 107.99;\r\nassert(abs(compoundPresent(F,r,n)-P)\u003c=1e-2)\r\n\r\n\r\n%%\r\nF = 184.74;\r\nr = 0.018;\r\nn = 5;\r\nP = 168.97;\r\nassert(abs(compoundPresent(F,r,n)-P)\u003c=1e-2)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":8703,"edited_by":8703,"edited_at":"2022-10-01T16:50:48.000Z","deleted_by":null,"deleted_at":null,"solvers_count":54,"test_suite_updated_at":"2022-10-01T16:49:27.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-09-30T05:16:46.000Z","updated_at":"2026-04-02T11:11:35.000Z","published_at":"2022-09-30T16:56:20.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTheorem : Compound Interest\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eF = P(1+r)^n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eF : Future value at the end of n periods\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eP : Present value\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003er : Annual nominal rate\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003en : Total number of compounding periods\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate P, given F, r and n. Round to the nearest cent.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":56090,"title":"Simple Interest : Calculate time in years","description":"Theorem : Simple Interest\r\n\r\nwhere;\r\nF : Future Value\r\nP : Present Value\r\nr : Annual simple interest rate (decimal)\r\nt : Time in years\r\nCalculate t, given F, P and r. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 213.741px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.997px 106.87px; transform-origin: 406.997px 106.87px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eTheorem : Simple Interest\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"88\" height=\"18.5\" style=\"width: 88px; height: 18.5px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ewhere;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7555px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 390.993px 40.8778px; transform-origin: 390.998px 40.8778px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eF : Future Value\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eP : Present Value\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003er : Annual simple interest rate (decimal)\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003et : Time in years\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eCalculate t, given F, P and r. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function t = simpleMaturity(F,P,r)\r\n\r\nend","test_suite":"%%\r\nF = 365;\r\nP = 100;\r\nr = 0.04;\r\nt = 66.25;\r\nassert(abs(simpleMaturity(F,P,r) - t) \u003c= 1e-2)\r\n\r\n%%\r\nF = 740;\r\nP = 500;\r\nr = 0.078;\r\nt = 6.15;\r\nassert(abs(simpleMaturity(F,P,r) - t )\u003c= 1e-2)\r\n\r\n\r\n%%\r\nF = 1400;\r\nP = 700;\r\nr = 0.014;\r\nt = 71.43;\r\nassert(abs(simpleMaturity(F,P,r) - t )\u003c= 1e-2)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":8703,"edited_by":8703,"edited_at":"2022-10-01T16:21:48.000Z","deleted_by":null,"deleted_at":null,"solvers_count":54,"test_suite_updated_at":"2022-10-01T16:21:48.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-09-29T18:52:22.000Z","updated_at":"2026-02-09T13:47:06.000Z","published_at":"2022-09-30T16:56:51.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTheorem : Simple Interest\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eF = P(1+rt)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eF : Future Value\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eP : Present Value\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003er : Annual simple interest rate (decimal)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003et : Time in years\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate t, given F, P and r. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":56075,"title":"Simple Interest : Calculate Future Value","description":"Theorem : Simple Interest\r\n\r\nwhere;\r\nF : Future Value\r\nP : Present Value\r\nr : Annual simple interest rate (decimal)\r\nt : Time in years\r\nCalculate F, given P, r and t. Round to nearest cent.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 213.741px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.997px 106.87px; transform-origin: 406.997px 106.87px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eTheorem : Simple Interest\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"88\" height=\"18.5\" style=\"width: 88px; height: 18.5px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ewhere;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7555px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 390.993px 40.8778px; transform-origin: 390.998px 40.8778px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eF : Future Value\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eP : Present Value\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003er : Annual simple interest rate (decimal)\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003et : Time in years\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eCalculate F, given P, r and t. Round to nearest cent.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function F = simpleFuture(P,r,t)\r\n \r\nend","test_suite":"%%\r\nP = 100;\r\nr = 0.12;\r\nt = 5;\r\ny_correct = 160;\r\nassert(abs( simpleFuture(P,r,t)-y_correct ) \u003c=1e-2)\r\n\r\n%%\r\nP = 140;\r\nr = 0.055;\r\nt = 3;\r\ny_correct = 163.1;\r\nassert(abs(simpleFuture(P,r,t)-y_correct)\u003c=1e-2)\r\n\r\n\r\n%%\r\nP = 12000;\r\nr = 0.045;\r\nt = 4;\r\ny_correct = 14160;\r\nassert(abs(simpleFuture(P,r,t)-y_correct)\u003c=1e-2)","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":8703,"edited_by":8703,"edited_at":"2022-10-01T16:18:34.000Z","deleted_by":null,"deleted_at":null,"solvers_count":50,"test_suite_updated_at":"2022-10-01T16:18:34.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-09-29T18:10:06.000Z","updated_at":"2026-03-30T22:48:20.000Z","published_at":"2022-09-30T16:57:41.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTheorem : Simple Interest\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eF = P(1+rt)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eF : Future Value\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eP : Present Value\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003er : Annual simple interest rate (decimal)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003et : Time in years\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate F, given P, r and t. Round to nearest cent.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":56095,"title":"Compound Interest : Future Value","description":"Theorem : Compound Interest\r\n\r\nwhere,\r\nF : Future value at the end of n periods\r\nP : Present value\r\nr : Annual nominal rate\r\nn : Total number of compounding periods\r\nCalculate F, given P, r and n. Round to the nearest cent.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 213.741px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.997px 106.87px; transform-origin: 406.997px 106.87px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eTheorem : Compound Interest\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"89\" height=\"19.5\" style=\"width: 89px; height: 19.5px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ewhere,\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7555px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 390.993px 40.8778px; transform-origin: 390.998px 40.8778px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eF : Future value at the end of n periods\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eP : Present value\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003er : Annual nominal rate\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003en : Total number of compounding periods\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eCalculate F, given P, r and n. Round to the nearest cent.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function F = compoundFuture(P,r,n)\r\n\r\nend","test_suite":"%%\r\nP = 100;\r\nr = 0.05;\r\nn = 30;\r\nF = 432.19;\r\nassert(abs(compoundFuture(P,r,n)-F)\u003c=1e-2)\r\n\r\n%%\r\nP = 850;\r\nr = 0.039;\r\nn = 14;\r\nF = 1452.23;\r\nassert(abs(compoundFuture(P,r,n)-F)\u003c=1e-2)\r\n\r\n%%\r\nP = 10000;\r\nr = 0.014;\r\nn = 12;\r\nF = 11815.59;\r\nassert(abs(compoundFuture(P,r,n)-F)\u003c=1e-2)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":8703,"edited_by":8703,"edited_at":"2022-10-01T16:22:56.000Z","deleted_by":null,"deleted_at":null,"solvers_count":79,"test_suite_updated_at":"2022-10-01T16:22:56.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-09-30T05:07:26.000Z","updated_at":"2026-02-06T15:37:13.000Z","published_at":"2022-09-30T16:56:35.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTheorem : Compound Interest\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eF = P(1+r)^n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eF : Future value at the end of n periods\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eP : Present value\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003er : Annual nominal rate\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003en : Total number of compounding periods\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate F, given P, r and n. Round to the nearest cent.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":56145,"title":"Ordinary Annuity : Present Value","description":"Theorem : Present Value of an Ordinary Annuity\r\n\r\nwhere;\r\nP : Present value of all payments\r\nA : Periodic payment\r\nr : Interest rate per period\r\nn : Number of periods (peyments)\r\nCalculate P, given A, r and n. Round to the nearest cent. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 230.377px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.997px 115.188px; transform-origin: 406.997px 115.188px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eTheorem : Present Value of an Ordinary Annuity\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 37.6379px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 18.8189px; text-align: left; transform-origin: 383.996px 18.8189px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-16px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"116\" height=\"37.5\" style=\"width: 116px; height: 37.5px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ewhere;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7555px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 390.993px 40.8778px; transform-origin: 390.998px 40.8778px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eP : Present value of all payments\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eA : Periodic payment\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003er : Interest rate per period\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003en : Number of periods (peyments)\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eCalculate P, given A, r and n. Round to the nearest cent. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function P = annuityPresent(A,r,n)\r\n\r\nend","test_suite":"%%\r\nA = 100;\r\nr = 0.004;\r\nn = 160;\r\nP = 11800.85\r\nassert(abs(annuityPresent(A,r,n) - P ) \u003c= 1e-2)\r\n\r\n%%\r\nA = 1500;\r\nr = 0.01;\r\nn = 24;\r\nP = 31865.08;\r\nassert(abs(annuityPresent(A,r,n) - P) \u003c= 1e-2)\r\n\r\n\r\n%%\r\nA = 1;\r\nr = 0.001;\r\nn = 100;\r\nP = 95.12;\r\nassert(abs(annuityPresent(A,r,n) - P) \u003c= 1e-2)","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":8703,"edited_by":8703,"edited_at":"2022-10-01T16:34:56.000Z","deleted_by":null,"deleted_at":null,"solvers_count":35,"test_suite_updated_at":"2022-10-01T16:34:56.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-09-30T07:57:13.000Z","updated_at":"2026-02-18T09:20:29.000Z","published_at":"2022-09-30T16:54:32.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTheorem : Present Value of an Ordinary Annuity\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eP = A \\\\frac{(1+r)^n-1}{r (1+r)^n}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eP : Present value of all payments\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA : Periodic payment\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003er : Interest rate per period\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003en : Number of periods (peyments)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate P, given A, r and n. Round to the nearest cent. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":56120,"title":"Compound Interest : Compounding Periods","description":"Theorem : Compound Interest\r\n\r\nwhere,\r\nF : Future value at the end of n periods\r\nP : Present value\r\nr : Annual nominal rate\r\nn : Total number of compounding periods\r\nCalculate n, given F, P and r. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 213.741px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.997px 106.87px; transform-origin: 406.997px 106.87px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eTheorem : Compound Interest\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"89\" height=\"19.5\" style=\"width: 89px; height: 19.5px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ewhere,\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7555px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 390.993px 40.8778px; transform-origin: 390.998px 40.8778px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eF : Future value at the end of n periods\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eP : Present value\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003er : Annual nominal rate\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003en : Total number of compounding periods\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eCalculate n, given F, P and r. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function n = compoundMaturity(F,P,r)\r\n\r\nend","test_suite":"%%\r\nF = 100;\r\nP = 50;\r\nr = 0.05;\r\nn = 14.21;\r\nassert(abs(compoundMaturity(F,P,r) - n ) \u003c= 1e-2)\r\n\r\n%%\r\nF = 1467;\r\nP = 467;\r\nr = 0.0123;\r\nn = 93.63;\r\nassert(abs(compoundMaturity(F,P,r) - n )\u003c= 1e-2)\r\n\r\n\r\n%%\r\nF = 1500;\r\nP = 380;\r\nr = 0.0567;\r\nn = 24.90;\r\nassert(abs(compoundMaturity(F,P,r) - n) \u003c= 1e-2)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":8703,"edited_by":8703,"edited_at":"2022-10-01T16:27:13.000Z","deleted_by":null,"deleted_at":null,"solvers_count":31,"test_suite_updated_at":"2022-10-01T16:27:13.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-09-30T05:22:51.000Z","updated_at":"2026-02-16T16:24:46.000Z","published_at":"2022-09-30T16:55:48.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTheorem : Compound Interest\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eF = P(1+r)^n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eF : Future value at the end of n periods\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eP : Present value\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003er : Annual nominal rate\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003en : Total number of compounding periods\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate n, given F, P and r. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":56080,"title":"Simple Interest : Calculate Present Value","description":"Theorem : Simple Interest\r\n\r\nwhere;\r\nF : Future Value\r\nP : Present Value\r\nr : Annual simple interest rate (decimal)\r\nt : Time in years\r\nCalculate P, given F, r and t. Round to nearest cent.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 213.741px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.997px 106.87px; transform-origin: 406.997px 106.87px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eTheorem : Simple Interest\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAALAAAAAlCAYAAADiHGOuAAAAAXNSR0IArs4c6QAAB5VJREFUeF7tnHnIfUUZxz9WlCIVZqKmUFBhoqQR2qYtUJllheKWpuZaoe1WWpmllkullJj7H+655ZJUKuJeEBWZ2qIFSqFEVi6llZrxgWdqPO85Z865773c9/zumX9+v3vPzJyZZ77zLN/nue9qjG2UwIAlsNqA1z4ufZQAI4BHEAxaAiOAB3184+JHAI8YGLQERgDP/vheALwKuB74z+xfN+g3bAw8C7i96y5GAHeV1GT9Xg58BPgK8KfJplioUc8BDgJ+BfwQeKq0+xKAXwbsAGwHbF2arPL8Q8CpPcfMq/t6wJ6FfT4C/AK4ETgf+E1BwBsBnwS+2BG8awP7AM8OwM9LFvN+rxrYS698iyAuATht5g3ALfHBg9ylZnIF/wrgEOB9wJuAm+YtjZ7vXyfA+dYYJ/iOAx4HXgp8IYCuDPz+G8BjNe9wnm/GBRbwbU3gfiAO7cUB+CN7rntV6678jgW+Bvy6bXNdAfzG0DzO5a3YA3igYeIt4/A8lN8OTLIvAs4D3gzcD7wb+Fm2h7WAM4Ht47v3R/98m88Mzas5PAZ4okEGPt8LWDf8vk8Azx0B/D9pibkD4mL/rQlHXQH8QeCUmORo4DDgyYZJNZ1qqo8CjS9eocB+NfA9YP2WiyrQjo/1nwF8DHg0288mwInAhwsXWKDblGOu+dX6s9DA7u2rwE/CRfnnnM9AV0ErrVv2l5q1eMG1cr8MpVG73C4AXgM4ARDEtvcCV7ZsXn/y9cBVwL/nLKS+r98dOLdwUfM+VwN+TgcgKA8Pjdp2yavr0o1Q828zQw2c3EDjEi9hnevTV16T9hd37wT2B/ZrseZvAz4TbpsWcUnrAmD9MoMWQXlb+L9Dcw26CFofXpPv4dp2BS6sGZgD+BzgQECf2JZk9SXg2i4vjT6LBGAx9w7g5MBV20VPLp0W7buTAthbcE0Mrh6YX6uhjwA0p0MGdu7/3g3sGOYrl5vC/3xm4hW+FFmie94TGlTw/24E8BIJrBmulW6S/n7Jmq8egfK/ghxYYtFLGrh0YK7w7RHUSBnN0yz1wEttV03sD0Kwl4Rpe6jScwPAS/wW4N4A+U+jj+6Dvqvcr2axOrZtfUPUwCquTWO/mwOvBXSp9LNfCHwc2Bu4APhy/F/gmtipts8BxlZ1TYuou7Eb8OdqhxKAnx+aVW1kexfwY+AZoXn12T4ddIfR+XKa2kxNvpy2HBcnD86qmtU1qTGkdgzOdBnkKvWXUzDr85PCn5NK7OP/DxHAulziwzxBCvBVZneFHMSKLT+TXCHWWfO6s9eqfb3BIhar0V4JqI3UKk2tydz2BeI8AZzAJz1o81+1se15gJSOvu4W4SapUS6uUGSJSZD77ssiDBHA6XzVvLqYpn+VkZb4rGByvh0Wy0DsHwF4XU0Vov0kB0otBZ+1eYWSBjZh8Z14QzV6lWrSXGg680CmtKCV+Fzqz4BtM+CvoUWkwwR2ysD9Hvh+mMmHazaR5jA46ZuBHDKAU1Cr/JTRPWG169LAuUJUW3cJdNMF0fLJ1DyttQE4+XSHxoi61LBa8+8db9JKBG5ak2bqivjQ1bRV95MAbPZoiaALm58GgPNLuBxZ9+Ghc+bGYiUD14OBugvumhLYfxQ+rXFEqbXKtQ3AOuIeppRHXVYqcZ4efJ6tKi1opT2vXtSupm0EMFQzl7IvTeUDuZz7cNETA7iUlRL8Fvv8ceDsQ35RdRe2BW6d4JYtoguRMzffiqSDlFddy+Xcp9Ar+cC1vHybBu6TPp7gvJcMmVcQl1/UG8LM3TfBhhYxiEvMjRff+pDrWuSW5GyXao1Jm7gTgLeqUyxNAK6mj+uKViY449Yh8wJwflGNivtSYGlTi0aj5czNZcC+hdqXJOdSMVgVJPrNnwV2jhLLTkFcnj6eFk02bcBPY75pXtTEccpkLEIiIw8aSy5BLuekJF4TLI/MTluTRFALS20uKQ5r0sB5+rgpKzUNAM17jmlfVOUmCyH92CetPg0WoiTLaRfzJOami4LLgz2t+c+jVNLCpybGwv0kLS81J/e+pAKyDsCWsZnf/1RIpK5ksCSsITx375onmRabRHytmeqxGbnxs6NQpbb4pGEufzMnj2rCqBQM9VjO07pOE8A5o9BFwSUuV0CKrQ0jdVy65Gp5KUldiFr/Ogewi5Iys8h6p2zrOuiWRhrgXAQ8OKkEV9A4zbw/IbLoPs/N3wxcHpmkuhrV0haUp4GNmt3sU1NE7jzK+3WRnvcXLI6xKW/BLK8qG9KFKy2ty+fTBHDOKHShHWWrTDd7US+NTOUfOixav9pyBf3n2tryUiauwzvGLhUJvCQycVatpUKflSCklVbQXpKJv345DTg9q4ZcMmYEcEmM/Z8rUzWq2sZfprRp4f6zL84I3TtdDy1ZY5XjCODZAMKo28o1U6aplmQ2b1o1Z/XvQxwVcZgBXGMbATw7AOhbG3wYJN4xu9escjP3ktsI4Nmev4chmyMjMeR6kdlK6f+zJ3n5E7Y7u7x0BHAXKS2vj7Sk9JpsQvEvzSzvVYMfLb2mv9uZARoBPPgzX+wNjABe7PMf/O5HAA/+CBd7AyOAF/v8B7/7/wKA0+k1FQ3SuwAAAABJRU5ErkJggg==\" width=\"88\" height=\"18.5\" style=\"width: 88px; height: 18.5px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ewhere;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7555px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 390.993px 40.8778px; transform-origin: 390.998px 40.8778px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eF : Future Value\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eP : Present Value\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003er : Annual simple interest rate (decimal)\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003et : Time in years\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eCalculate P, given F, r and t. Round to nearest cent.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function P = simplePresent(F,r,t)\r\n\r\nend","test_suite":"%%\r\nF = 100;\r\nr = 0.045;\r\nt = 4;\r\ny_correct = 84.75;\r\nassert(abs(simplePresent(F,r,t)-y_correct)\u003c=1e-2)\r\n\r\n%%\r\nF = 48;\r\nr = 0.11;\r\nt = 90;\r\ny_correct = 4.40;\r\nassert(abs(simplePresent(F,r,t)-y_correct)\u003c=1e-2)\r\n\r\n\r\n%%\r\nF = 140000;\r\nr = 0.04;\r\nt = 7;\r\ny_correct = 109375;\r\nassert(abs(simplePresent(F,r,t)-y_correct)\u003c=1e-2)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":8703,"edited_by":8703,"edited_at":"2022-10-01T16:19:38.000Z","deleted_by":null,"deleted_at":null,"solvers_count":48,"test_suite_updated_at":"2022-10-01T16:19:38.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-09-29T18:31:37.000Z","updated_at":"2026-02-16T12:18:29.000Z","published_at":"2022-09-30T16:57:26.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTheorem : Simple Interest\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eF = P(1+rt)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eF : Future Value\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eP : Present Value\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003er : Annual simple interest rate (decimal)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003et : Time in years\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate P, given F, r and t. Round to nearest cent.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":56085,"title":"Simple Interest : Calculate annual simple interest rate","description":"Theorem : Simple Interest\r\n\r\nwhere;\r\nF : Future Value\r\nP : Present Value\r\nr : Annual simple interest rate (decimal)\r\nt : Time in years\r\nCalculate r, given F, P and t.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 213.741px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.997px 106.87px; transform-origin: 406.997px 106.87px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eTheorem : Simple Interest\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"88\" height=\"18.5\" style=\"width: 88px; height: 18.5px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ewhere;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7555px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 390.993px 40.8778px; transform-origin: 390.998px 40.8778px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eF : Future Value\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eP : Present Value\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003er : Annual simple interest rate (decimal)\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003et : Time in years\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eCalculate r, given F, P and t.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function r = simpleRate(F,P,t)\r\n\r\nend","test_suite":"%%\r\nF = 500;\r\nP = 100;\r\nt = 6;\r\nr = 0.6667;\r\nassert(abs(simpleRate(F,P,t)-r) \u003c= 1e-2)\r\n\r\n%%\r\nF = 360000;\r\nP = 300000;\r\nt = 15;\r\nr = 0.0133;\r\nassert(abs(simpleRate(F,P,t)-r )\u003c= 1e-2)\r\n\r\n\r\n%%\r\nF = 2250;\r\nP = 1000;\r\nt = 7;\r\nr = 0.1786;\r\nassert(abs(simpleRate(F,P,t)-r) \u003c= 1e-2)","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":8703,"edited_by":8703,"edited_at":"2022-10-01T16:20:49.000Z","deleted_by":null,"deleted_at":null,"solvers_count":44,"test_suite_updated_at":"2022-10-01T16:20:49.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-09-29T18:44:04.000Z","updated_at":"2026-02-16T12:16:52.000Z","published_at":"2022-09-30T16:57:09.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTheorem : Simple Interest\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eF = P(1+rt)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eF : Future Value\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eP : Present Value\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003er : Annual simple interest rate (decimal)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003et : Time in years\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate r, given F, P and t.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":56125,"title":"Ordinary Annuity : Future Value","description":"Theorem : Future Value of an Ordinary Annuity \r\n\r\nwhere;\r\nF : Future value\r\nA : Periodic payment\r\nr : Rate per period\r\nn : Number of periods (payments)\r\nCalculate F, given, A, r and n. Round to the nearest cent.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 229.056px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.997px 114.522px; transform-origin: 406.997px 114.528px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eTheorem : Future Value of an Ordinary Annuity \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 36.3166px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 18.1526px; text-align: left; transform-origin: 383.996px 18.1583px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"117.5\" height=\"36.5\" style=\"width: 117.5px; height: 36.5px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ewhere;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7555px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 390.993px 40.8778px; transform-origin: 390.998px 40.8778px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eF : Future value\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eA : Periodic payment\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003er : Rate per period\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003en : Number of periods (payments)\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eCalculate F, given, A, r and n. Round to the nearest cent.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function F = annuityFuture(A,r,n)\r\n\r\nend","test_suite":"%%\r\nA = 150;\r\nr = 0.055;\r\nn = 15;\r\nF = 3361.30;\r\nassert(abs(annuityFuture(A,r,n) - F) \u003c= 1e-2)\r\n\r\n%%\r\nA = 4000;\r\nr = 0.017;\r\nn = 55;\r\nF = 359358.70;\r\nassert(abs(annuityFuture(A,r,n) - F) \u003c= 1e-2)\r\n\r\n\r\n%%\r\nA = 120;\r\nr = 0.041;\r\nn = 4;\r\nF = 510.34;\r\nassert(abs(annuityFuture(A,r,n) - F )\u003c= 1e-2)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":8703,"edited_by":8703,"edited_at":"2022-10-01T16:37:51.000Z","deleted_by":null,"deleted_at":null,"solvers_count":48,"test_suite_updated_at":"2022-10-01T16:37:51.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-09-30T05:37:05.000Z","updated_at":"2026-02-17T08:42:39.000Z","published_at":"2022-09-30T16:55:31.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTheorem : Future Value of an Ordinary Annuity \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eF = A \\\\frac{(1+r)^n -1}{r}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eF : Future value\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA : Periodic payment\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003er : Rate per period\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003en : Number of periods (payments)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate F, given, A, r and n. Round to the nearest cent.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":56130,"title":"Ordinary Annuity : Periodic Payments (Future Value)","description":"Theorem : Future Value of an Ordinary Annuity \r\n\r\nwhere;\r\nF : Future value\r\nA : Periodic payment\r\nr : Rate per period\r\nn : Number of periods (payments)\r\nCalculate A, given, F, r and n. Round to the nearest cent.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 229.056px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.997px 114.522px; transform-origin: 406.997px 114.528px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eTheorem : Future Value of an Ordinary Annuity \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 36.3166px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 18.1526px; text-align: left; transform-origin: 383.996px 18.1583px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"117.5\" height=\"36.5\" style=\"width: 117.5px; height: 36.5px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ewhere;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7555px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 390.993px 40.8778px; transform-origin: 390.998px 40.8778px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eF : Future value\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eA : Periodic payment\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003er : Rate per period\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003en : Number of periods (payments)\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eCalculate A, given, F, r and n. Round to the nearest cent.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function A = annuityFPayment(F,r,n)\r\n\r\nend","test_suite":"%%\r\nF = 5000;\r\nr = 0.02;\r\nn = 9;\r\nA = 512.58;\r\nassert(abs(annuityFPayment(F,r,n) - A) \u003c= 1e-2)\r\n\r\n%%\r\nF = 1457.85;\r\nr = 0.07;\r\nn = 15;\r\nA = 58.01;\r\nassert(abs(annuityFPayment(F,r,n) - A) \u003c= 1e-2)\r\n\r\n\r\n%%\r\nF = 1e6;\r\nr = 0.1;\r\nn = 30;\r\nA = 6079.25;\r\nassert(abs(annuityFPayment(F,r,n) - A) \u003c= 1e-2)","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":8703,"edited_by":8703,"edited_at":"2022-10-01T16:29:58.000Z","deleted_by":null,"deleted_at":null,"solvers_count":47,"test_suite_updated_at":"2022-10-01T16:29:58.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-09-30T05:43:13.000Z","updated_at":"2026-02-18T09:27:30.000Z","published_at":"2022-09-30T16:55:14.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTheorem : Future Value of an Ordinary Annuity \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eF = A \\\\frac{(1+r)^n -1}{r}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eF : Future value\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA : Periodic payment\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003er : Rate per period\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003en : Number of periods (payments)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate A, given, F, r and n. Round to the nearest cent.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":56105,"title":"Compound Interest: Interest Rate","description":"Theorem : Compound Interest\r\n\r\nwhere,\r\nF : Future value at the end of n periods\r\nP : Present value\r\nr : Annual nominal rate\r\nn : Total number of compounding periods\r\nCalculate r, given F, P and n. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 213.741px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.997px 106.87px; transform-origin: 406.997px 106.87px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eTheorem : Compound Interest\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"89\" height=\"19.5\" style=\"width: 89px; height: 19.5px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ewhere,\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7555px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 390.993px 40.8778px; transform-origin: 390.998px 40.8778px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eF : Future value at the end of n periods\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eP : Present value\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003er : Annual nominal rate\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003en : Total number of compounding periods\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eCalculate r, given F, P and n. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function r = compoundRate(F,P,n)\r\n\r\nend","test_suite":"%%\r\nF = 500;\r\nP = 100;\r\nn = 10;\r\nr = 0.1746;\r\nassert(abs(compoundRate(F,P,n)-r) \u003c= 1e-2)\r\n\r\n%%\r\nF = 10000;\r\nP = 9000;\r\nn = 2;\r\nr = 0.054;\r\nassert(abs(compoundRate(F,P,n)-r )\u003c= 1e-2)\r\n\r\n\r\n%%\r\nF = 320;\r\nP = 40;\r\nn = 75;\r\nr = 0.0281;\r\nassert(abs(compoundRate(F,P,n)-r )\u003c= 1e-2)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":8703,"edited_by":8703,"edited_at":"2022-10-01T16:26:10.000Z","deleted_by":null,"deleted_at":null,"solvers_count":60,"test_suite_updated_at":"2022-10-01T16:26:10.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-09-30T05:20:21.000Z","updated_at":"2026-02-16T16:39:39.000Z","published_at":"2022-09-30T16:56:03.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTheorem : Compound Interest\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eF = P(1+r)^n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eF : Future value at the end of n periods\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eP : Present value\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003er : Annual nominal rate\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003en : Total number of compounding periods\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate r, given F, P and n. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":56140,"title":"Ordinary Annuity : Number of payments (Future Value)","description":"Theorem : Future Value of an Ordinary Annuity \r\n\r\nwhere;\r\nF : Future value\r\nA : Periodic payment\r\nr : Rate per period\r\nn : Number of periods (payments)\r\nCalculate n, given, F, A and r. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 229.056px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.997px 114.522px; transform-origin: 406.997px 114.528px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eTheorem : Future Value of an Ordinary Annuity \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 36.3166px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 18.1526px; text-align: left; transform-origin: 383.996px 18.1583px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"117.5\" height=\"36.5\" style=\"width: 117.5px; height: 36.5px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ewhere;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7555px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 390.993px 40.8778px; transform-origin: 390.998px 40.8778px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eF : Future value\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eA : Periodic payment\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003er : Rate per period\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003en : Number of periods (payments)\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eCalculate n, given, F, A and r. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function n = annuityFMaturity(F,A,r)\r\n\r\nend","test_suite":"%%\r\nF = 500000;\r\nA = 10000;\r\nr = 0.085\r\nn = 20.33;\r\nassert(abs(annuityFMaturity(F,A,r) - n) \u003c= 1e-2)\r\n\r\n%%\r\nF = 100;\r\nA = 1;\r\nr = 0.074\r\nn = 29.81;\r\nassert(abs(annuityFMaturity(F,A,r) - n) \u003c= 1e-2)\r\n\r\n\r\n%%\r\nF = 1000;\r\nA = 0.1;\r\nr = 0.052\r\nn = 123.40;\r\nassert(abs(annuityFMaturity(F,A,r) - n )\u003c= 1e-2)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":8703,"edited_by":8703,"edited_at":"2022-10-01T16:30:39.000Z","deleted_by":null,"deleted_at":null,"solvers_count":30,"test_suite_updated_at":"2022-10-01T16:30:39.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-09-30T07:39:23.000Z","updated_at":"2026-02-17T09:03:03.000Z","published_at":"2022-09-30T16:54:47.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTheorem : Future Value of an Ordinary Annuity \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eF = A \\\\frac{(1+r)^n -1}{r}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eF : Future value\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA : Periodic payment\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003er : Rate per period\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003en : Number of periods (payments)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate n, given, F, A and r. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":56165,"title":"Ordinary Annuity : Number of Payments (Present Value)","description":"Theorem : Present Value of an Ordinary Annuity\r\n\r\nwhere;\r\nP : Present value of all payments\r\nA : Periodic payment\r\nr : Interest rate per period\r\nn : Number of periods (peyments)\r\nCalculate n, given P, A and r. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 230.733px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 115.367px; transform-origin: 407px 115.367px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 151.5px 8px; transform-origin: 151.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eTheorem : Present Value of an Ordinary Annuity\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 38px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 19px; text-align: left; transform-origin: 384px 19px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-16px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 116px; height: 38px;\" width=\"116\" height=\"38\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21px 8px; transform-origin: 21px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7333px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 391px 40.8667px; transform-origin: 391px 40.8667px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 103.5px 8px; transform-origin: 103.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eP : Present value of all payments\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 65px 8px; transform-origin: 65px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA : Periodic payment\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 81px 8px; transform-origin: 81px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003er : Interest rate per period\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 105.5px 8px; transform-origin: 105.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003en : Number of periods (peyments)\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 92.5px 8px; transform-origin: 92.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCalculate n, given P, A and r. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function n = annuityPMaturity(P,A,r)\r\n \r\nend","test_suite":"%%\r\nP = 1200;\r\nA = 500;\r\nr = 0.05;\r\nn = 2.62;\r\nassert(abs(annuityPMaturity(P,A,r) - n )\u003c= 1e-2)\r\n\r\n%%\r\nP = 10000;\r\nA = 1500;\r\nr = 0.0075;\r\nn = 6.86;\r\nassert(abs(annuityPMaturity(P,A,r) - n) \u003c= 1e-2)\r\n\r\n\r\n%%\r\nP = 400;\r\nA = 20;\r\nr = 0.0025;\r\nn = 20.54;\r\nassert(abs(annuityPMaturity(P,A,r) - n) \u003c= 1e-2)\r\n\r\n%%\r\nP = randi(10)*1e3;\r\nA = 2*P;\r\nr = 1;\r\nn = 1;\r\nassert(abs(annuityPMaturity(P,A,r) - n) \u003c= 1e-2)\r\n\r\n%%\r\nP = randi(10)*3e3;\r\nA = 4*P/3;\r\nr = 1;\r\nn = 2;\r\nassert(abs(annuityPMaturity(P,A,r) - n) \u003c= 1e-2)","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":8703,"edited_by":223089,"edited_at":"2022-12-19T07:56:40.000Z","deleted_by":null,"deleted_at":null,"solvers_count":22,"test_suite_updated_at":"2022-12-19T07:56:40.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-09-30T16:36:30.000Z","updated_at":"2026-02-18T10:17:09.000Z","published_at":"2022-09-30T16:53:13.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTheorem : Present Value of an Ordinary Annuity\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eP = A \\\\frac{(1+r)^n-1}{r (1+r)^n}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eP : Present value of all payments\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA : Periodic payment\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003er : Interest rate per period\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003en : Number of periods (peyments)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate n, given P, A and r. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":56160,"title":"Ordinary Annuity : Rate (Present Value)","description":"Theorem : Present Value of an Ordinary Annuity\r\n\r\nwhere;\r\nP : Present value of all payments\r\nA : Periodic payment\r\nr : Interest rate per period\r\nn : Number of periods (peyments)\r\nCalculate r, given P, A and n. Assume interest rate is in [0, 1].","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 230.377px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.997px 115.188px; transform-origin: 406.997px 115.188px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eTheorem : Present Value of an Ordinary Annuity\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 37.6379px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 18.8189px; text-align: left; transform-origin: 383.996px 18.8189px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-16px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"116\" height=\"37.5\" style=\"width: 116px; height: 37.5px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ewhere;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7555px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 390.993px 40.8778px; transform-origin: 390.998px 40.8778px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eP : Present value of all payments\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eA : Periodic payment\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003er : Interest rate per period\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4389px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 362.994px 10.2137px; text-align: left; transform-origin: 363px 10.2194px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003en : Number of periods (peyments)\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21.0018px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.996px 10.5009px; text-align: left; transform-origin: 383.996px 10.5009px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eCalculate r, given P, A and n. Assume interest rate is in [0, 1].\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function r = annuityPRate(P,A,n)\r\n\r\nend","test_suite":"%%\r\nP = 650000;\r\nA = 65000;\r\nn = 25;\r\nr =0.0878;\r\nassert(abs(annuityPRate(P,A,n) - r )\u003c= 1e-4)\r\n\r\n\r\n%%\r\nP = 10000;\r\nA = 1000;\r\nn = 12;\r\nr =0.0292;\r\nassert(abs(annuityPRate(P,A,n) - r) \u003c= 1e-4)\r\n\r\n%%\r\nP = 50000;\r\nA = 250;\r\nn = 360;\r\nr =0.0037;\r\nassert(abs(annuityPRate(P,A,n) - r) \u003c= 1e-4)\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":8703,"edited_by":8703,"edited_at":"2022-10-01T16:33:28.000Z","deleted_by":null,"deleted_at":null,"solvers_count":14,"test_suite_updated_at":"2022-10-01T16:33:28.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-09-30T15:59:26.000Z","updated_at":"2022-10-01T16:33:34.000Z","published_at":"2022-09-30T16:53:23.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTheorem : Present Value of an Ordinary Annuity\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eP = A \\\\frac{(1+r)^n-1}{r (1+r)^n}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eP : Present value of all payments\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA : Periodic payment\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003er : Interest rate per period\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003en : Number of periods (peyments)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate r, given P, A and n. Assume interest rate is in [0, 1].\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":56135,"title":"Ordinary Annuity : Rate (Future Value)","description":"Theorem : Future Value of an Ordinary Annuity \r\n\r\nwhere;\r\nF : Future value\r\nA : Periodic payment\r\nr : Rate per period\r\nn : Number of periods (payments)\r\nCalculate r, given, F, A and n. Assume interest rate is a positive real number. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 229.233px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 114.617px; transform-origin: 407px 114.617px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 150px 8px; transform-origin: 150px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eTheorem : Future Value of an Ordinary Annuity \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 36.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 18.25px; text-align: left; transform-origin: 384px 18.25px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 117.5px; height: 36.5px;\" width=\"117.5\" height=\"36.5\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21px 8px; transform-origin: 21px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7333px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 391px 40.8667px; transform-origin: 391px 40.8667px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 50.5px 8px; transform-origin: 50.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eF : Future value\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 65px 8px; transform-origin: 65px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA : Periodic payment\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 58px 8px; transform-origin: 58px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003er : Rate per period\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 105.5px 8px; transform-origin: 105.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003en : Number of periods (payments)\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 242px 8px; transform-origin: 242px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCalculate r, given, F, A and n. Assume interest rate is a positive real number. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function r = annuityFRate(F,A,n)\r\n \r\nend","test_suite":"%%\r\nfiletext = fileread('annuityFRate.m');\r\nillegal = contains(filetext, 'switch') || contains(filetext, 'if')\r\nassert(~illegal)\r\n\r\n%%\r\nF = 500000;\r\nA = 1000;\r\nn = 45;\r\nr = 0.0884;\r\nassert(abs(annuityFRate(F,A,n) - r) \u003c= 1e-4)\r\n\r\n%%\r\nF = 60000;\r\nA = 1500;\r\nn = 20;\r\nr = 0.0677;\r\nassert(abs(annuityFRate(F,A,n) - r) \u003c= 1e-4)\r\n\r\n\r\n%%\r\nF = 125000;\r\nA = 400;\r\nn = 120;\r\nr = 0.0142;\r\nassert(abs(annuityFRate(F,A,n) - r )\u003c= 1e-4)\r\n\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":5,"created_by":8703,"edited_by":223089,"edited_at":"2022-12-12T06:15:30.000Z","deleted_by":null,"deleted_at":null,"solvers_count":17,"test_suite_updated_at":"2022-12-12T06:15:30.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-09-30T05:52:00.000Z","updated_at":"2022-12-12T06:15:31.000Z","published_at":"2022-09-30T16:55:04.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTheorem : Future Value of an Ordinary Annuity \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eF = A \\\\frac{(1+r)^n -1}{r}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eF : Future value\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA : Periodic payment\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003er : Rate per period\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003en : Number of periods (payments)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate r, given, F, A and n. Assume interest rate is a positive real number. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"term":"tag:\"mathematics of finance\"","current_player_id":null,"fields":[{"name":"page","type":"integer","callback":null,"default":1,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":null,"prepend":true},{"name":"per_page","type":"integer","callback":null,"default":50,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":null,"prepend":true},{"name":"sort","type":"string","callback":null,"default":null,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":null,"prepend":true},{"name":"body","type":"text","callback":null,"default":"*:*","directive":null,"facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":false},{"name":"group","type":"string","callback":null,"default":null,"directive":"group","facet":true,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"difficulty_rating_bin","type":"string","callback":null,"default":null,"directive":"difficulty_rating_bin","facet":true,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"id","type":"integer","callback":null,"default":null,"directive":"id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"tag","type":"string","callback":null,"default":null,"directive":"tag","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"product","type":"string","callback":null,"default":null,"directive":"product","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"created_at","type":"timeframe","callback":{},"default":null,"directive":"created_at","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"profile_id","type":"integer","callback":null,"default":null,"directive":"author_id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"created_by","type":"string","callback":null,"default":null,"directive":"author","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"player_id","type":"integer","callback":null,"default":null,"directive":"solver_id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"player","type":"string","callback":null,"default":null,"directive":"solver","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"solvers_count","type":"integer","callback":null,"default":null,"directive":"solvers_count","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"comments_count","type":"integer","callback":null,"default":null,"directive":"comments_count","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"likes_count","type":"integer","callback":null,"default":null,"directive":"likes_count","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"leader_id","type":"integer","callback":null,"default":null,"directive":"leader_id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"leading_solution","type":"integer","callback":null,"default":null,"directive":"leading_solution","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true}],"filters":[{"name":"asset_type","type":"string","callback":null,"default":null,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":"\"cody:problem\"","prepend":true},{"name":"profile_id","type":"integer","callback":{},"default":null,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":"author_id","static":null,"prepend":true}],"query":{"params":{"per_page":50,"term":"tag:\"mathematics of finance\"","current_player":null,"sort":"map(difficulty_value,0,0,999) asc"},"parser":"MathWorks::Search::Solr::QueryParser","directives":{"term":{"directives":{"tag":[["tag:\"mathematics of finance\"","","\"","mathematics of finance","\""]]}}},"facets":{"#\u003cMathWorks::Search::Field:0x00007f46043dff08\u003e":null,"#\u003cMathWorks::Search::Field:0x00007f46043dfe68\u003e":null},"filters":{"#\u003cMathWorks::Search::Field:0x00007f46043df5a8\u003e":"\"cody:problem\""},"fields":{"#\u003cMathWorks::Search::Field:0x00007f45e7670280\u003e":1,"#\u003cMathWorks::Search::Field:0x00007f45e76701e0\u003e":50,"#\u003cMathWorks::Search::Field:0x00007f45e7670140\u003e":"map(difficulty_value,0,0,999) asc","#\u003cMathWorks::Search::Field:0x00007f45e76700a0\u003e":"tag:\"mathematics of finance\""},"user_query":{"#\u003cMathWorks::Search::Field:0x00007f45e76700a0\u003e":"tag:\"mathematics of finance\""},"queried_facets":{}},"query_backend":{"connection":{"configuration":{"index_url":"http://index-op-v2/solr/","query_url":"http://search-op-v2/solr/","direct_access_index_urls":["http://index-op-v2/solr/"],"direct_access_query_urls":["http://search-op-v2/solr/"],"timeout":10,"vhost":"search","exchange":"search.topic","heartbeat":30,"pre_index_mode":false,"host":"rabbitmq-eks","port":5672,"username":"search","password":"J3bGPZzQ7asjJcCk","virtual_host":"search","indexer":"amqp","http_logging":"true","core":"cody"},"query_connection":{"uri":"http://search-op-v2/solr/cody/","proxy":null,"connection":{"parallel_manager":null,"headers":{"User-Agent":"Faraday v1.0.1"},"params":{},"options":{"params_encoder":"Faraday::FlatParamsEncoder","proxy":null,"bind":null,"timeout":null,"open_timeout":null,"read_timeout":null,"write_timeout":null,"boundary":null,"oauth":null,"context":null,"on_data":null},"ssl":{"verify":true,"ca_file":null,"ca_path":null,"verify_mode":null,"cert_store":null,"client_cert":null,"client_key":null,"certificate":null,"private_key":null,"verify_depth":null,"version":null,"min_version":null,"max_version":null},"default_parallel_manager":null,"builder":{"adapter":{"name":"Faraday::Adapter::NetHttp","args":[],"block":null},"handlers":[{"name":"Faraday::Response::RaiseError","args":[],"block":null}],"app":{"app":{"ssl_cert_store":{"verify_callback":null,"error":null,"error_string":null,"chain":null,"time":null},"app":{},"connection_options":{},"config_block":null}}},"url_prefix":"http://search-op-v2/solr/cody/","manual_proxy":false,"proxy":null},"update_format":"RSolr::JSON::Generator","update_path":"update","options":{"url":"http://search-op-v2/solr/cody"}}},"query":{"params":{"per_page":50,"term":"tag:\"mathematics of finance\"","current_player":null,"sort":"map(difficulty_value,0,0,999) asc"},"parser":"MathWorks::Search::Solr::QueryParser","directives":{"term":{"directives":{"tag":[["tag:\"mathematics of finance\"","","\"","mathematics of finance","\""]]}}},"facets":{"#\u003cMathWorks::Search::Field:0x00007f46043dff08\u003e":null,"#\u003cMathWorks::Search::Field:0x00007f46043dfe68\u003e":null},"filters":{"#\u003cMathWorks::Search::Field:0x00007f46043df5a8\u003e":"\"cody:problem\""},"fields":{"#\u003cMathWorks::Search::Field:0x00007f45e7670280\u003e":1,"#\u003cMathWorks::Search::Field:0x00007f45e76701e0\u003e":50,"#\u003cMathWorks::Search::Field:0x00007f45e7670140\u003e":"map(difficulty_value,0,0,999) asc","#\u003cMathWorks::Search::Field:0x00007f45e76700a0\u003e":"tag:\"mathematics of finance\""},"user_query":{"#\u003cMathWorks::Search::Field:0x00007f45e76700a0\u003e":"tag:\"mathematics of finance\""},"queried_facets":{}},"options":{"fields":["id","difficulty_rating"]},"join":" "},"results":[{"id":56150,"difficulty_rating":"easy"},{"id":56100,"difficulty_rating":"easy"},{"id":56090,"difficulty_rating":"easy"},{"id":56075,"difficulty_rating":"easy"},{"id":56095,"difficulty_rating":"easy"},{"id":56145,"difficulty_rating":"easy"},{"id":56120,"difficulty_rating":"easy"},{"id":56080,"difficulty_rating":"easy"},{"id":56085,"difficulty_rating":"easy"},{"id":56125,"difficulty_rating":"easy"},{"id":56130,"difficulty_rating":"easy"},{"id":56105,"difficulty_rating":"easy"},{"id":56140,"difficulty_rating":"easy"},{"id":56165,"difficulty_rating":"easy"},{"id":56160,"difficulty_rating":"easy-medium"},{"id":56135,"difficulty_rating":"easy-medium"}]}}