Question
What will be the difference between S.I. and C.I. on a sum of Rs. 15000 for 2 years at the same rate of interest of $$12\frac{1}{2}$$ % per annum ?
Answer: Option B
$$\eqalign{
& {\text{S}}{\text{.I}}{\text{. = Rs}}{\text{. }}\left( {15000 \times \frac{{25}}{2} \times 2 \times \frac{1}{{100}}} \right) \cr
& \,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. }}3750 \cr
& {\text{C}}{\text{.I}}{\text{. = Rs}}{\text{. }}\left[ {15000{{\left( {1 + \frac{{25}}{{2 \times 100}}} \right)}^2} - 15000} \right] \cr
& = {\text{Rs}}{\text{. }}\left( {15000 \times \frac{9}{8} \times \frac{9}{8} - 15000} \right) \cr
& = {\text{Rs}}{\text{. }}\left( {18948.375 - 15000} \right) \cr
& = {\text{Rs}}{\text{. }}3984.375 \cr
& {\text{Difference }} \cr
& {\text{ = Rs}}{\text{. }}\left( {3984.375 - 3750} \right) \cr
& = {\text{Rs}}{\text{. }}234.375 \cr} $$
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$$\eqalign{
& {\text{S}}{\text{.I}}{\text{. = Rs}}{\text{. }}\left( {15000 \times \frac{{25}}{2} \times 2 \times \frac{1}{{100}}} \right) \cr
& \,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. }}3750 \cr
& {\text{C}}{\text{.I}}{\text{. = Rs}}{\text{. }}\left[ {15000{{\left( {1 + \frac{{25}}{{2 \times 100}}} \right)}^2} - 15000} \right] \cr
& = {\text{Rs}}{\text{. }}\left( {15000 \times \frac{9}{8} \times \frac{9}{8} - 15000} \right) \cr
& = {\text{Rs}}{\text{. }}\left( {18948.375 - 15000} \right) \cr
& = {\text{Rs}}{\text{. }}3984.375 \cr
& {\text{Difference }} \cr
& {\text{ = Rs}}{\text{. }}\left( {3984.375 - 3750} \right) \cr
& = {\text{Rs}}{\text{. }}234.375 \cr} $$
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