A sum of money at compound interest doubles itself in 15 years. It will become eight times of itself in · ABC26GN4192

$P\left(1+\frac{R}{100}\right)^{15}=2 P \Rightarrow\left(1+\frac{R}{100}\right)^{15}=2$ Let $P\left(1+\frac{R}{100}\right)^{n}=8 P$ $$\begin{aligned} & \Rightarrow\left(1+\frac{R}{100}\right)^{n}=8=2^{3}=\left\{\left(1+\frac{R}{100}\right)^{15}\right\}^{3} \\ & \Rightarrow\left(1+\frac{R}{100}\right)^{n}=\left(1+\frac{R}{100}\right)^{45} \Rightarrow n=45 . \end{aligned}$$ ∴ Required time $=45$ years.