Discussion
What will be the difference between simple and compound interest at 10% per annum on a sum of Rs. 1000 after 4 years?
Answer: D
\[ A = P\left(1 + \frac{R}{100}\right)^{n}, \qquad \text{CI} = A - P, \qquad \text{SI} = \frac{PRn}{100} \]
\[ \text{SI} = 1000 \times 0.10 \times 4 = \text{Rs. } 400 \]
\[ \text{CI} = 1000\left[(1.1)^{4} - 1\right] = 1000(1.4641 - 1) = \text{Rs. } 464.10 \]
\[ \text{difference} = 464.10 - 400 = \text{Rs. } 64.10 \]
The gap widens sharply with time: over three years it is only Rs. 31, and over two years Rs. 10. That growth is the compounding acting on ever more accumulated interest.
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