Question

Juan doubled his $4.000 in years. At which rate of return did Juan double his investment?

Answer 1

For this problem we can use the future value formula given by:

$A=P(1+\frac{r}{n})^{nt}$

Where P= 4000 represent the initial amount

A= 8000 represent the amount doubled

t= 8 represent the number of years

n= 12 assuming that the interest is compounded each year

r= represent the rate of interest that we want to find

So then we need to solve for r

$8000\text{=4000(1+}\frac{r}{12})^{^{12\cdot8}}$

If we divide both sides by 4000 we got:

$2=(1+\frac{r}{12})^{96}$

We apply exponentiation on both sides and we got:

$2^{1/96}=(1+\frac{r}{12})$$r=\text{ (}2^{1/96}-1)\cdot12=\text{ 0.08695}\rightarrow8.7$