Question

A certain sum of money, lent out at compound interest, amounts to Rs. 14,520 in 2 years and to Rs. 17,569.20 in 4 years. Find the rate of interest per annum and the sum.

Answer 1

Amount in 2 years= Rs. 14,520 $\Rightarrow P{(1+\frac{r}{100})}^2=14250$.........(i)
Amount in 4 years = Rs. 17569.20 $\Rightarrow P{(1+\frac{r}{100})}^4=17569.20$........(ii)
On dividing (ii) by (i), we get :
$\frac{P{(1+\frac{r}{100})}^4}{P{(1+\frac{r}{100})}^2}=\frac{17569.20}{14250}$

$\Rightarrow {(1+\frac{r}{100})}^2=\frac{121}{100}$ (on simplifying)
$\Rightarrow 1+\frac{r}{100}=\frac{11}{10}\Rightarrow r=10$
Now, $P{(1+\frac{r}{100})}^2=14520$

$\Rightarrow P{(1+\frac{10}{100})}^2=14520$
$\Rightarrow P\times \frac{121}{100}=14520$

$P=14520\times \frac{100}{121}=12000$
$\therefore$ Rate of interest = 10% and sum = Rs. 12,000