Question
A bank offers 5% compound interest calculated on half yearly basis. A customer deposits Rs.1600 each on 1st January and 1st July of a year. At the end of the year, the amount he would have gained by way of interest is = ?
Answer: Option B
$$\eqalign{
& {\text{ = Rs}}.\left[ {1600 \times {{\left( {1 + \frac{5}{{2 \times 100}}} \right)}^2} + 1600 \times \left( {1 + \frac{5}{{2 \times 100}}} \right)} \right] \cr
& {\text{ = Rs}}.\left[ {1600 \times \frac{{41}}{{40}} \times \frac{{41}}{{40}} + 1600 \times \frac{{41}}{{40}}} \right] \cr
& {\text{ = Rs}}.\left[ {1600 \times \frac{{41}}{{40}}\left( {\frac{{41}}{{40}} + 1} \right)} \right] \cr
& {\text{ = Rs}}.\left( {\frac{{1600 \times 41 \times 81}}{{40 \times 40}}} \right) \cr
& {\text{ = Rs}}.\,3321 \cr
& \therefore {\text{C}}{\text{.I}}{\text{. = Rs}}.\left( {3321 - 3200} \right) \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}.\,121 \cr} $$
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$$\eqalign{
& {\text{ = Rs}}.\left[ {1600 \times {{\left( {1 + \frac{5}{{2 \times 100}}} \right)}^2} + 1600 \times \left( {1 + \frac{5}{{2 \times 100}}} \right)} \right] \cr
& {\text{ = Rs}}.\left[ {1600 \times \frac{{41}}{{40}} \times \frac{{41}}{{40}} + 1600 \times \frac{{41}}{{40}}} \right] \cr
& {\text{ = Rs}}.\left[ {1600 \times \frac{{41}}{{40}}\left( {\frac{{41}}{{40}} + 1} \right)} \right] \cr
& {\text{ = Rs}}.\left( {\frac{{1600 \times 41 \times 81}}{{40 \times 40}}} \right) \cr
& {\text{ = Rs}}.\,3321 \cr
& \therefore {\text{C}}{\text{.I}}{\text{. = Rs}}.\left( {3321 - 3200} \right) \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}.\,121 \cr} $$
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