Discussion
Sam invested Rs. 15000 @ 10% per annum for one year. If the interest is compounded half-yearly, then the amount received by Sam at the end of the year will be?
Answer: C
\[ A = P\left(1 + \frac{R}{100}\right)^{n}, \qquad \text{CI} = A - P, \qquad \text{SI} = \frac{PRn}{100} \]
Half-yearly compounding halves the rate and doubles the number of periods.
\[ \text{rate} = 5\% \text{ per half-year}, \qquad n = 2 \]
\[ A = 15000 \times (1.05)^{2} = 15000 \times 1.1025 = \text{Rs. } 16{,}537.50 \]
Annual compounding at 10% would give Rs. 16,500; the extra Rs. 37.50 is the second half-year's 5% on the first half-year's Rs. 750.
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