Question

The difference between the compounded annually and the simple interest on a certain sum for $2$ years at $4\%$ per annum is $Rs.20$. Find the sum?

Answer 1

From question,

Difference between Compound and Simple interest, $=Rs20$

Time $=2$ years

Rate of Interest, $R=4\%$

The difference between compound interest and simple interest on certain sum (say $P$) for $2$ years then

Difference $=P{\left(\frac{R}{100}\right)}^2$

$\Rightarrow 20=P{\left(\frac{4}{100}\right)}^2$

$\Rightarrow 20=P(\frac{1}{25}{)}^2$

$\Rightarrow 20=P\left(\frac{1}{625}\right)$

$\Rightarrow 20=\frac{P}{625}$

$\Rightarrow P=625\times 20$

$\Rightarrow P=12500$

Hence, the required sum is $Rs.12,500$.