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+(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+}(r)/(12))^{^(12\cdot8)}`

If we divide both sides by 4000 we got:

`2=(1+(r)/(12))^(96)`

We apply exponentiation on both sides and we got:

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