For this problem we can use the future value formula given by:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]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
[tex]8000\text{=4000(1+}\frac{r}{12})^{^{12\cdot8}}[/tex]If we divide both sides by 4000 we got:
[tex]2=(1+\frac{r}{12})^{96}[/tex]We apply exponentiation on both sides and we got:
[tex]2^{1/96}=(1+\frac{r}{12})[/tex][tex]r=\text{ (}2^{1/96}-1)\cdot12=\text{ 0.08695}\rightarrow8.7[/tex]