Question

A sum of money, invested at compound interest, amounts to Rs. $19,360$ in $2$ years and to Rs. $23,425.60$ in $4$ years. Find the original sum of money.

Answer 1

On interest being compounded for $2$ years, $Amount=P{(1+\frac{R}{100})}^N$
$⟹19,360=P{(1+\frac{R}{100})}^2$ --- (1)
On interest being compounded for $4$ years, $Amount=P{(1+\frac{R}{100})}^N$
$⟹23,425.60=P{(1+\frac{R}{100})}^4$ --- (2)
Dividing, eqn (2) by eqn (1)
$1.21={(1+\frac{R}{100})}^2$
Taking square root on both sides,
$1.1=1+\frac{R}{100}$
$⟹0.1=\frac{R}{100}$
$⟹R=10$ %
Putting the value of $R$ in eqn $\left(1\right),$ we get
$⟹19,360=P{(1+\frac{10}{100})}^2$
$⟹19,360=P\times (1.1{)}^2$
$⟹P=\frac{19,360}{1.21}$
$⟹P=Rs.16,000$