How to find time period of compound interest using a formula

Question

I am making a compound interest calculator, and want to input minimum 3 input fields from "amount", "compound interest", "time" and "rate". I can calculate the remaining field by the data provided but the problem comes when I have to find the value of "time".

Now, take a simple example of p = $1000, r =10% pa and A = 1210. I know that the answer for time is 2 years, but I have to use a formula. After I searched, I got formula:

t = log10(A/P) / (n*log10(1+R/n))

Here n is how much times I have to compound annually, i.e. 1 times so it is 1. So formula will become

t= log10(1210/1000)/1*log10(1+10/1)

which ultimately is log10(1.21)/log10(11).

Now putting it in JavaScript, const t = Math.log10(1.21)/Math.log10(11) gives answer as 0.079494864421745, while the actual time is 2.

What am I doing wrong?

R should not be 10, as in "ten percent". You'l have better luck if you enter it as 0.10. That gives your answer of 2. — duffymo, Jun 09 '22 at 15:38
Yes, but now instead of getting 2, i am getting 1.9999999999999982. — Ajinkya Kamble, Jun 09 '22 at 15:58
You're welcome. https://stackoverflow.com/questions/588004/is-floating-point-math-broken/588014#588014 — duffymo, Jun 09 '22 at 15:59

score 0 · Answer 1 · answered Jun 13 '22 at 12:09

0

Instead of 10 you need to use 1.1, since:

1000 * 1.1^x = 1210
1.1^x = 1210/1000
x = log1.1(1210/1000)
x = 2

answered Jun 13 '22 at 12:09

Boris Kaptsanov

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How to find time period of compound interest using a formula

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