Question

A sum amounts to $Rs23762$ in $2$ years at $9\%$ per annum, compounded annually. Find the sum.

Answer 1

Amount $\left(A\right)=Rs23762$
Rate of interest $\left(R\right)=9\%$
Time $\left(n\right)=2$ years
Now, $A=P\times (1+\frac{R}{100}{)}^n$
$\Rightarrow Rs23762=P\times (1+\frac{9}{100}{)}^2$
$\Rightarrow Rs23762=P(\frac{109}{100}{)}^2$
$\Rightarrow P=Rs23762\times \frac{100\times 100}{109\times 109}$
$\Rightarrow P=Rs23762\times \frac{10000}{11881}$
$\Rightarrow P=2\times 10000$
$\Rightarrow P=Rs20000$

Therefore, the principal amount is $Rs20,000$.