Question

A sum of money doubles itself in $8$ years at compound interest. It will amount to $16$ times itself at the same rate of interest in:

Answer 1

Let the principal be $P$ and the rate be$r$

According to the question,

$2P=P{(1+\frac{r}{100})}^{8}2={(1+\frac{r}{100})}^8$

Raising to the power of $4$ on both sides,

$$\begin{gathered} 2^4=[{(1+\frac{r}{100})}^8{]}^4 \\ 16P=P{(1+\frac{r}{100})}^{32} \end{gathered}$$

Therefore, in $32$ years the principal will become $16$ times itself.