Question

At compound interest, if a certain sum of money doubles in n years, then the amount will be four fold in :

• A. $n^2$ years
• B. $2n^2$ years
• C. 2n years
• D. 4n years

Answer 1

The correct option is C 2n years

Since, A = 2P, then
$2P=P{(1+\frac{r}{100})}^n\Rightarrow 2={(1+\frac{r}{100}))}^n\Rightarrow 4=(2{)}^2={\left[{(1+\frac{r}{100})}^n\right]}^2=\left[{(1+\frac{r}{100})}^{2n}\right]$
$\Rightarrow$ time period = 2n years $\{\because (a^m{)}^n=a^{m.n}\}$
(This question can be easily done by considering some appropriate values)