Discussion
A sum invested at 10% p.a. for 2 years becomes ₹ 3,267, when the interest is compounded annually. What will be the simple interest on the same sum at the same rate in \(2\frac{1}{2}\) years ?
Answer: C
The simple interest is ₹ 675.
First find the principal from the compound amount, then apply simple interest for 2.5 years:
\[ \begin{aligned} P(1.1)^2 &= 3267 \Rightarrow P = \frac{3267}{1.21} = 2700 \\ SI &= \frac{2700 \times 10 \times 2.5}{100} = 675 \end{aligned} \]
₹ 625, ₹ 650 and ₹ 700 come from a wrong principal or period; for example interest on 2,600 for 2.5 years would be 650.
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