Discussion
Rajiv invested a sum of ₹ 7,000 at 20% p.a. for \(1\frac{1}{2}\) years, compounded half yearly, and his friend Amit invested a sum of ₹ 8,000 at 10% p.a. for 2 years, compounded annually. What is the difference between the interest received by Rajiv and Amit, at maturity ?
Answer: C
The difference is ₹ 637.
Rajiv: 20% a year compounded half-yearly is 10% per half-year, for 3 half-years.
\[ \begin{aligned} A &= 7000 \times (1.1)^3 \\ &= 7000 \times 1.331 = 9317 \end{aligned} \]
So Rajiv's interest is ₹ 2,317. Amit: 10% a year compounded annually for 2 years.
\[ \begin{aligned} A &= 8000 \times (1.1)^2 \\ &= 8000 \times 1.21 = 9680 \end{aligned} \]
Amit's interest is ₹ 1,680, and \(2317 - 1680 = 637\). Treating Rajiv's investment as compounded yearly at 20% would give a quite different figure, which is why the half-yearly rate and period must both be halved and doubled.
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