how to calculate number of years in compound interest

Question

I'm trying to calculate the number of years in compound interest, but I find that the online formula can't get the answer I want. I don't know why. Does anyone know what the specific formula is? I know the calculator can done that, but I need to use formula for programming.

The formula I use is $n = \dfrac{\ln(FV / PV)}{\ln(1 + r)}$, but the result is $15.114$ something, but not as what the picture shows.

This is what suppose to be:

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score 1 · Accepted Answer · answered Aug 12 '22 at 08:58

1

Because the interest in compounded half-yearly, the $r$ in your equation is $6.45\%/2$. This is how they arrive at their answer.

However, I think the question and model answer are a bit misleading. I'd usually say that the half-yearly interest is $(1+r)^{1/2}-1$, for an annual interest of $r$.

answered Aug 12 '22 at 08:58

Philip Winchester

134

so how should I use formula to find the results? – python learner Aug 12 '22 at 09:02
Set $r = 6.45%/2$. Then $N = \ln{(10000/4000)}/\ln{(1+ 6.45%/2)}$ – Philip Winchester Aug 12 '22 at 09:03
okokok,got it, thx – python learner Aug 12 '22 at 09:05

how to calculate number of years in compound interest

1 Answers1