Question

A sum of money amounts to $Rs10240$ in $2$ years at $6\frac{2}{3}\%$ per annum, compounded annually. Find the sum.

Answer 1

Let $P$ be the sum.

Rate of interest, $R=6\frac{2}{3}\%=\frac{20}{3}\%$
Time $t=2$ years
Given amount, $A=Rs.10240$

Since, we have compound interest formula $A=P(1+\frac{R}{100}{)}^2$
Substitute values of $R,t$ and $A$ in above equation,
$\Rightarrow 10240=P{(1+\frac{\left(\frac{20}{3}\right)}{100})}^2$
$\Rightarrow 10240=P{(1+\frac{1}{15})}^2$
$\Rightarrow 10240=P{\left(\frac{15+1}{15}\right)}^2$
$\Rightarrow 10240=P{\left(\frac{16}{15}\right)}^2$
$\Rightarrow 10240\left(\frac{15\times 15}{16\times 16}\right)=P$
$\Rightarrow P=40\times 225$
Thus, $P=Rs.9000$
Hence, the required sum is $Rs.9000$