Discussion

Find the C.I. on a sum of Rs.1600 for 9 months at 20% per annum, interest being 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 counts quarters instead of years.

\[ \text{rate} = \frac{20}{4} = 5\% \text{ per quarter}, \qquad n = \frac{9}{3} = 3 \text{ quarters} \]

\[ A = 1600 \times (1.05)^{3} = 1600 \times 1.157625 = \text{Rs. } 1852.20 \]

\[ \text{CI} = 1852.20 - 1600 = \text{Rs. } 252.20 \]

Nine months is three quarters, not nine periods - using \( n = 9 \) would wildly overstate the interest.

No comment is present. Be the first to comment.

Loading…