Discussion
Find the C.I. on Rs. 15,625 for 9 months at 16% per annum compounded quarterly?
Answer: C
\[ A = P\left(1 + \frac{R}{100}\right)^{n}, \qquad \text{CI} = A - P, \qquad \text{SI} = \frac{PRn}{100} \]
Quarterly compounding quarters the rate, and nine months is three quarters.
\[ \text{rate} = \frac{16}{4} = 4\% \text{ per quarter}, \qquad n = 3 \]
\[ A = 15625 \times (1.04)^{3} = 15625 \times 1.124864 = \text{Rs. } 17{,}576 \]
\[ \text{CI} = 17576 - 15625 = \text{Rs. } 1951 \]
The principal is \( 25^{3} \) and the amount \( 26^{3} \), since the factor is \( \left(\tfrac{26}{25}\right)^{3} \) - which is why both come out as whole numbers.
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