Question

A sum of money placed at compound interest doubles itself in $4$ years. It will amount to eight times in:

• A. $8years$
• B. $10years$
• C. $12years$
• D. $16years$

Answer 1

The correct option is C $12years$

Let, the sum of money be P. It doubles itself in 4 years.

Let, the rate of interest be r %

For compound interest we know,

Total amount $=P{(1+\frac{r}{100})}^n$ [where n is the time]

According to the question,

$2P=P{(1+\frac{r}{100})}^4$

$\Rightarrow 2={(1+\frac{r}{100})}^4$ ----eq.1

Again, let, to be the eight times the needed time is n years.

Hence by formula we get,

$8P=P{(1+\frac{r}{100})}^n$

$\Rightarrow 8={(1+\frac{r}{100})}^n$ ----eq.2

From eq.1 we get, $(1+\frac{r}{100})=2^{1/4}$ ----eq.3

piutting this value in eq.2 we get,

$8={\left(2^{1/4}\right)}^n\Rightarrow 2^3=2^{\frac{n}{4}}$

Comparing both sides we get, $3=\frac{n}{4}\Rightarrow n=12years.$

$\therefore$ option C is correct.