Discussion
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: B
\[ A = P\left(1 + \frac{R}{100}\right)^{n}, \qquad \text{CI} = A - P, \qquad \text{SI} = \frac{PRn}{100} \]
Half-yearly compounding at 5% per annum means 2.5% per half-year. The January deposit earns for two half-years and the July deposit for one.
\[ A = 1600(1.025)^{2} + 1600(1.025) \]
\[ = 1600(1.050625) + 1640 = 1681 + 1640 = \text{Rs. } 3321 \]
\[ \text{interest} = 3321 - 3200 = \text{Rs. } 121 \]
Each deposit must be tracked from its own date; treating the full Rs. 3200 as present all year would give Rs. 162.
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