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

The difference between the simple interset and compound interest on a certain sum of money 'P' for 2 years at $r\%$ per annum is given by :

$\Rightarrow {(CI-SI)}_{2year}=\frac{P{r}^2}{{100}^2}$

Using the above formula for a sum of money 'P' invested for two years at $4\%$ p.a., given that the difference between $CI\&SI$ is $Rs.20$

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

$\Rightarrow 20=\frac{P(4\times 4)}{100\times 100}$

$\Rightarrow 5\times 25\times 100=P$

$\Rightarrow P=Rs.12500$

Hence, the answer is $Rs.12500.$