Discussion
Rs. 400 is simple interest for a sum for 4 years at 10% rate of interest per annum. Find the compound interest for the same sum at same rate of interest for same time period?
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 first.
\[ 400 = \frac{P \times 10 \times 4}{100} = 0.4P \quad\Longrightarrow\quad P = \text{Rs. } 1000 \]
\[ \text{CI} = 1000\left[(1.1)^{4} - 1\right] = 1000(1.4641 - 1) \]
\[ = \text{Rs. } 464.10 \]
The Rs. 64.10 by which compound exceeds simple interest is all the interest earned on earlier interest.
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