Discussion

Simple interest on a sum at 4% per annum for 2 years is Rs.80. The C.I. on the same sum for the same period is?

Answer: A

\[ A = P\left(1 + \frac{R}{100}\right)^{n}, \qquad \text{CI} = A - P, \qquad \text{SI} = \frac{PRn}{100} \]

Recover the principal from the simple interest.

\[ 80 = \frac{P \times 4 \times 2}{100} = 0.08P \quad\Longrightarrow\quad P = \text{Rs. } 1000 \]

\[ \text{CI} = 1000\left[(1.04)^{2} - 1\right] = 1000(1.0816 - 1) = \text{Rs. } 81.60 \]

The Rs. 1.60 excess is 4% of the first year's Rs. 40 of interest - the whole of what compounding adds over two years.

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