# How long will it take you to triple your money if you invest it at a rate 6% compounded annually?

Apr 2, 2015

It will approximately take 18 years 10 months.

The compound interest formula is:

$A = P \cdot {\left(1 + \left(\frac{r}{n}\right)\right)}^{n t}$

Where:

$P$ is the initial amount
$r$ is annual rate of interest
$t$ is number of years
$A$ is the final amount of money
$n$ is the number of times the interest is compounded per year

So we want to find $t$. Lets start

$3 \cdot P = P \cdot {\left(1 + 0.06\right)}^{t}$
$3 = {1.06}^{t}$

Now we should use logarithmic functions.

$\ln \left(3\right) = t \cdot \ln \left(1.06\right)$

$\ln \frac{3}{\ln} \left(1.06\right) = t$

$t = 18.85$

So the answer is approximately 18 years 10 months.