Discussion
Sarang invested some money in HDFC at 3% rate of interest. What would be the corresponding simple interest if after 2 years, Sarang got Rs. 101.50 as compound interest?
Answer: C
\[ A = P\left(1 + \frac{R}{100}\right)^{n}, \qquad \text{CI} = A - P, \qquad \text{SI} = \frac{PRn}{100} \]
Recover the principal from the compound interest first.
\[ \text{CI} = P\left[(1.03)^{2} - 1\right] = P(0.0609) = 101.50 \]
\[ P = \frac{101.50}{0.0609} = \text{Rs. } 1666.67 \]
\[ \text{SI} = 1666.67 \times 0.03 \times 2 = \text{Rs. } 100 \]
The Rs. 1.50 gap between the two is interest on the first year's Rs. 50 of interest - which is the whole of what compounding adds over two years.
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