The difference between simple interest ans compound interest on Rs. P at R% p.a in 2 years is = ?

Solution (By Examveda Team)

$$\eqalign{ & {\text{S}}{\text{.I}}{\text{. = Rs}}{\text{.}}\left( {\frac{{P \times R \times 2}}{{100}}} \right) \cr & \,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\left( {\frac{{2PR}}{{100}}} \right) \cr & {\text{C}}{\text{.I}}{\text{. = Rs}}{\text{.}}\left[ {P \times {{\left( {1 + \frac{R}{{100}}} \right)}^2} - P} \right] \cr & \,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\left[ {\frac{{P{R^2}}}{{{{\left( {100} \right)}^2}}} + \frac{{2PR}}{{100}}} \right] \cr & \therefore {\text{Difference}} \cr & {\text{ = Rs}}{\text{.}}\left[ {\left\{ {\frac{{P{R^2}}}{{{{\left( {100} \right)}^2}}} + \frac{{2PR}}{{100}}} \right\} - \frac{{2PR}}{{100}}} \right] \cr & = {\text{Rs}}{\text{.}}\left[ {\frac{{P{R^2}}}{{{{\left( {100} \right)}^2}}}} \right] \cr} $$