Question

A sum of money at compound interest (compounded annually) doubles itself in $4$ years. In how many years will it amount to eight times of itself ?

• A. 12 years
• B. 10 years
• C. 8 years
• D. 16 years

Answer 1

Answer: (A)

12 years

Given,

$2P=P{(1+\frac{R}{100})}^4\Rightarrow {(1+\frac{R}{100})}^4=2......\left(1\right)$
Let the time in which it amounts to eight times of itself be $r$ years
Then,

$8P=P{(1+\frac{R}{100})}^r\Rightarrow {(1+\frac{R}{100})}^r=8=2^3$
${(1+\frac{R}{100})}^r=2^3={\left({(1+\frac{R}{100})}^4\right)}^3$ from $\left(1\right)$
${(1+\frac{R}{100})}^r={(1+\frac{R}{100})}^{12}$

Bases are equal, $⟹r=12$ years

$\therefore r=12$ years