Question

The difference between simple interest and compound interest on a certain sum of money for $2$ years at $4\%$ per annum is $Rs20$. Find the sum.

Answer 1

Compound interest $=P[{(1+\frac{r}{100})}^t-1]$ and Simple interest $=\frac{P\times r\times t}{100}$

$\therefore =P[{(1+\frac{r}{100})}^t-1]-\frac{Prt}{100}=20P[{(1+\frac{4}{100})}^2-1-\frac{4\times 2}{100}]=20P\times .0016=20P=\frac{20}{.0016}$

$⟹P=\text{Rs}\frac{20\times 10000}{16}⟹P=\text{Rs}12500$

$\therefore$ the sum is $\text{Rs}12500$