The difference between simple interest ans compound interest on Rs. P at R% p.a in 2 years is = ?
A. $${\text{Rs}}{\text{.}}\,\frac{{PR}}{{100}}$$
B. $${\text{Rs}}{\text{.}}\,\frac{{2PR}}{{100}}$$
C. $${\text{Rs}}{\text{.}}\,\frac{{P{R^2}}}{{100}}$$
D. $${\text{Rs}}{\text{.}}\,\frac{{P{R^2}}}{{{{\left( {100} \right)}^2}}}$$
Answer: Option D
Solution(By Examveda Team)
$$\eqalign{ & {\text{S}}{\text{.I}}{\text{. = Rs}}{\text{.}}\left( {\frac{{P \times R \times 2}}{{100}}} \right) \cr & \,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\left( {\frac{{2PR}}{{100}}} \right) \cr & {\text{C}}{\text{.I}}{\text{. = Rs}}{\text{.}}\left[ {P \times {{\left( {1 + \frac{R}{{100}}} \right)}^2} - P} \right] \cr & \,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\left[ {\frac{{P{R^2}}}{{{{\left( {100} \right)}^2}}} + \frac{{2PR}}{{100}}} \right] \cr & \therefore {\text{Difference}} \cr & {\text{ = Rs}}{\text{.}}\left[ {\left\{ {\frac{{P{R^2}}}{{{{\left( {100} \right)}^2}}} + \frac{{2PR}}{{100}}} \right\} - \frac{{2PR}}{{100}}} \right] \cr & = {\text{Rs}}{\text{.}}\left[ {\frac{{P{R^2}}}{{{{\left( {100} \right)}^2}}}} \right] \cr} $$Related Questions on Compound Interest
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