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Question

A bank offers $$5\%$$ compound interest calculated on half-yearly basis. A customer deposits $$Rs. 1600$$ each on $$1^{st}$$ January and $$1^{st}$$ July of a year. At the end of the year, the amount he would have gained by way of interest is:


A
Rs.120
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B
Rs.121
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C
Rs.122
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D
Rs.123
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Solution

The correct option is B $$Rs. 121$$
$$Amount = Rs. \left [1600\times \left (1 + \dfrac {5}{2\times 100}\right )^{2} + 1600\times \left (1 + \dfrac {5}{2\times 100}\right )\right ]$$
$$= Rs. \left [1600\times \dfrac {41}{40} \times \dfrac {41}{40} + 1600\times \dfrac {41}{60}\right ]$$
$$= Rs. \left [1600\times \dfrac {41}{40}\left (\dfrac {41}{40} + 1\right )\right ]$$
$$= Rs. \left [\dfrac {1600\times 41\times 81}{40\times 40}\right ]$$
$$= Rs. 3321$$.
$$\therefore C.I. = Rs. (3321 - 3200) = Rs. 121$$

Mathematics

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