Question

A sum of money doubles itself in $3$ years at CI, when the interest is compounded annually. In how many years will the sum amount to $16$ times of itself?

• A. 6 years
• B. 8 years
• C. 12 years
• D. 16 years

Answer 1

The correct option is C

12 years

Therefore,
$2p=p{(1+\frac{R}{100})}^n$

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

$\Rightarrow 1+\frac{R}{100}=2^{\frac{1}{3}}\dots \dots \left(1\right)$

Assume the money becomes $16$ times itself in $n$ years.

$\Rightarrow 16p=p{(1+\frac{R}{100})}^n$