Question

A sum of money doubles itself at compound interest in 15 years. Then number of years required to make it eight times is

• A. 33 years
• B. 40 years
• C. 45 years
• D. 50 years

Answer 1

The correct option is C 45 years

Let the sum be $x$ and $CI=2x$

We know that

$CI=P(1+\frac{R}{100}{)}^T$

$2x=x(1+\frac{R}{100}{)}^{15}$

$(1+\frac{R}{100}{)}^{15}=2$ $.............\left(1\right)$

Let $m$ be the number of years.

Therefore,

$x(1+\frac{R}{100}{)}^m=8x$

$(1+\frac{R}{100}{)}^m=2^3$

$(1+\frac{R}{100}{)}^m=[(1+\frac{R}{100}{)}^{15}{]}^3$ $Frome{q}^n\left(1\right)$

$(1+\frac{R}{100}{)}^m=(1+\frac{R}{100}{)}^{45}$

On comparing both power, we get

$m=45years$

Hence, this is the answer.