How to calculate compound interest?

A person deposits $1000 in a bank. Interest is compounded monthly at the rate of 1% per month. I'm trying to write a program that will compute the monthly balance, but only on an annual basis, for 10 years. I want too vectorize it if possible. I've heard about using nest loops but I don't know how. I

[Adam]

Work out any solution first, then when it works improve it afterwards. For people experienced in that going straight for a vectorised approach makes sense, but for others doing a solution with for loops and understanding how that works before converting it to a vectorised approach is easier.

[Kevin]

Ok I'll try that

Answer 1

[Alexandra Harkai]

Vectorizing it would be smart, this page says it all: https://uk.mathworks.com/help/matlab/matlab_prog/vectorization.html

Answer 2

[Thorsten]

If you have amount A at an interest rate of r, you have after one month

A + rA = A(1 + r)

after two months

 A(1+r) + rA(1+r) = A(1+r)(1+r) = A(1+r)^2

after three months

 A(1+r)^2 + rA(1+r)^2 = A(1+r)^2(1+r) = A(1+r)^3

So after n month you have

A(1+r)^n

And after N years you have

 A(1+r)^(N*12)

in your case

 1000 * (1.01)^120 = 3300.39

So with some basic math you can directly compute the solution without any need for loops or vectorisation.

Answer 3

[SUDHARSHAN REDDY MARUDI]

1000 * (1.01)^120 = 3300.39

Answer 4

[SURAJ PATIL]

x=1000;
y=0.1;
t=2;
d=x*(1+y)^t;

Answer 5

[Fardin Khan]

A person places $20,000 in a savings account which pays 5 percent interest perannum, compounded continuously. Find

(a) the solution of the dollar balance in the account at any time

[Walter Roberson]

No, this is not a solution to the problem.