If the simple interest on a sum of money for 2 years at 5% per annum is Rs. 50, what is the compound interest on the same at the same rate and for the same time?

Solution(By Examveda Team)

$$\eqalign{ & {\text{Sum}} = Rs.\,\left( {\frac{{50 \times 100}}{{2 \times 5}}} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,500 \cr & {\text{Amount}} = Rs.\,\left[ {500 \times {{\left( {1 + \frac{5}{{100}}} \right)}^2}} \right] \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,\left( {500 \times \frac{{21}}{{20}} \times \frac{{21}}{{20}}} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,551.25 \cr & \therefore {\text{C}}{\text{.I}}{\text{.}} = Rs.\,\left( {551.25 - 500} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,51.25 \cr} $$