Question

A sum of money triples itself at compound interest in 12 years. In how many years will it become 9 times?

• A. 24 years
• B. 36 years
• C. 48 years
• D. None of these

Answer 1

The correct option is A

24 years

P${(1+\frac{R}{100})}^{12}=3P$

$\Rightarrow$${(1+\frac{R}{100})}^{15}$=$\frac{3P}{P}$ = 3$\dots \dots \left(i\right)$

Let P${(1+\frac{R}{100})}^n$=9P

$\Rightarrow$${(1+\frac{R}{100})}^n=9$

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

$\Rightarrow$${(1+\frac{R}{100})}^n$ = ${\left\{{(1+\frac{R}{100})}^{12}\right\}}^2$ {using(i)}

$\Rightarrow$${(1+\frac{R}{100})}^n$ = ${(1+\frac{R}{100})}^{24}$

$\Rightarrow$ n = 24

Thus, the required time = 24 years.