Question

A sum of money at compound interest amounts thrice itself in 3 years. In how many years will it be times itself?

• A. 12
• B. 9
• C. 6
• D. 8

Answer 1

The correct option is C 6

$\begin{array}{cc}P{(1+\frac{R}{100})}^3& =3P\Rightarrow {(1+\frac{R}{100})}^3=3\cdots \left(i\right)\\ LetP{(1+\frac{R}{100})}^n& =9P\Rightarrow {(1+\frac{R}{100})}^n=9.\\ \therefore {(1+\frac{R}{100})}^n& =3^2\&={\left[{(1+\frac{R}{100})}^3\right]}^2=(1+\frac{R}{100})\left\{using\right(i\left)\right\}\\ & \text{Hence, n = 6 years.}\end{array}$