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
b) Rs. 121
c) Rs. 122
d) Rs. 123

Answer: b
Explanation:
$$\eqalign{ & {\text{Amount}} = {1600 \times {{\left( {1 + \frac{5}{{2 \times 100}}} \right)}^2} + 1600 \times \left( {1 + \frac{5}{{2 \times 100}}} \right)} \cr & = {1600 \times \frac{{41}}{{40}} \times \frac{{41}}{{40}} + 1600 \times \frac{{41}}{{40}}} \cr & = {1600 \times \frac{{41}}{{40}}\left( {\frac{{41}}{{40}} + 1} \right)} \cr & = {\frac{{1600 \times 41 \times 81}}{{40 \times 40}}} \cr & = Rs.\,3321 \cr & C.I. = Rs.\,\left( {3321 – 3200} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,121 \cr} $$