Question

A sum of money doubles itself at compound interest in 15 years. In how many years will it become eight times?

• A. 40
• B. 41
• C. 45
• D. 50

Answer 1

The correct option is C

45

$P(1+\frac{R}{100}{)}^{1}5=2P\Rightarrow (1+\frac{R}{100}{)}^{15}=\frac{2P}{P}=2$ ...........(i)
Let $P(1+\frac{R}{100}{)}^n=8P\Rightarrow (1+\frac{R}{100}{)}^n=8=2^3=\left(\right(1+\frac{R}{100}{)}^{15}{)}^3$ {using (i)}
$\Rightarrow (1+\frac{R}{100}{)}^n=(1+\frac{R}{100}{)}^{45}\Rightarrow n=45$.
Thus, the required time = 45 years.