Question

A sum of money placed at compound interest doubles itself in $4$ years. In how many years will it amount to $8$ times?

• A. $6years$
• B. $8years$
• C. $12years$
• D. $10years$

Answer 1

The correct option is C $12years$

We know that,
$Amount=P{(1+\frac{R}{100})}^n$
Case - I:
$2=1{(1+\frac{R}{100})}^4....\left(1\right)$
Case - II:
$8=1{(1+\frac{R}{100})}^n$
$2^3=1{(1+\frac{R}{100})}^n$
${\left[{(1+\frac{R}{100})}^4\right]}^3={(1+\frac{R}{100})}^n$ (from eq. $\left(1\right)$)
${(1+\frac{R}{100})}^{12}={(1+\frac{R}{100})}^n$
On comparing, we get $n=12years$.