# Thread: In its first 10 years a mutual fund produced an average annual return of 21.38%

1. ## In its first 10 years a mutual fund produced an average annual return of 21.38%

Assume that money invested in this fund continues to earn 21.38%
compounded annually. How long will it take money invested in this fund to double?

It will take approximately 4 years for the money invested in this fund to double.

How do I find the number of years here?

I realize I put the answer here. I just need the formula, and the steps.

2. ## Re: In its first 10 years a mutual fund produced an average annual return of 21.38%

let $c$ be the initial amount invested

$2c = c(1+0.2138)^n$

$2 = 1.2138^n$

$\ln(2) = n \ln(1.2138)$

$n = \dfrac{\ln(2)}{\ln(1.2138)} \approx 3.5774 \approx 4$