Question
A man gets a simple interest on Rs. 1000 on a certain principal at the rate of 5 p.c.p.a. in 4 years. What compound interest will the man get on twice the principal in 2 years at the same rate ?
Answer: Option E
$$\eqalign{
& {\text{Principal}} \cr
& {\text{ = Rs}}{\text{.}}\left( {\frac{{100 \times 1000}}{{5 \times 4}}} \right) \cr
& = {\text{Rs}}{\text{. 5}}000 \cr
& {\text{Now, P = Rs}}{\text{.}}\,10000, \cr
& {\text{T = 2 years,}} \cr
& {\text{R = 5% }} \cr
& {\text{Amount}} \cr
& {\text{ = Rs}}{\text{.}}\left[ {10000 \times {{\left( {1 + \frac{5}{{100}}} \right)}^2}} \right] \cr
& = {\text{Rs}}{\text{.}}\left( {10000 \times \frac{{21}}{{20}} \times \frac{{21}}{{20}}} \right) \cr
& = {\text{Rs}}. 11025 \cr
& \therefore {\text{C}}{\text{.I}}{\text{. = }}\left( {11025 - 10000} \right) \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}. 1025 \cr} $$
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$$\eqalign{
& {\text{Principal}} \cr
& {\text{ = Rs}}{\text{.}}\left( {\frac{{100 \times 1000}}{{5 \times 4}}} \right) \cr
& = {\text{Rs}}{\text{. 5}}000 \cr
& {\text{Now, P = Rs}}{\text{.}}\,10000, \cr
& {\text{T = 2 years,}} \cr
& {\text{R = 5% }} \cr
& {\text{Amount}} \cr
& {\text{ = Rs}}{\text{.}}\left[ {10000 \times {{\left( {1 + \frac{5}{{100}}} \right)}^2}} \right] \cr
& = {\text{Rs}}{\text{.}}\left( {10000 \times \frac{{21}}{{20}} \times \frac{{21}}{{20}}} \right) \cr
& = {\text{Rs}}. 11025 \cr
& \therefore {\text{C}}{\text{.I}}{\text{. = }}\left( {11025 - 10000} \right) \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}. 1025 \cr} $$
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