A sum of money placed at $C.I$  double itself in $5years$ . In how many year, it would amount to $8times$  of itself at the same rate of interest?

Let principal be $\text{'}P\text{'}$ , then $A=2P$

$2P=P{\left(1+\frac{R}{100}\right)}^5$

$\Rightarrow$ ${\left(1+\frac{R}{100}\right)}^5=2$

$\Rightarrow$ $\left(1+\frac{R}{100}\right)=2^{\frac{1}{5}}$

It would be $8times$

(i.e) $8P=P{\left(1+\frac{R}{100}\right)}^n$

$8={\left(2^{\frac{1}{5}}\right)}^n$

$\Rightarrow$ $2^3=2^{\frac{n}{5}}$

$\Rightarrow$ $\frac{n}{5}=3$

$\Rightarrow$ $n=15$