Discussion
What will be the difference between simple interest and compound interest @ 10% per annum on a sum of Rs. 1000 after 3 years?
Answer: A
\[ A = P\left(1 + \frac{R}{100}\right)^{n}, \qquad \text{CI} = A - P, \qquad \text{SI} = \frac{PRn}{100} \]
\[ \text{SI} = 1000 \times 0.10 \times 3 = \text{Rs. } 300 \]
\[ \text{CI} = 1000\left[(1.1)^{3} - 1\right] = 1000(1.331 - 1) = \text{Rs. } 331 \]
\[ \text{difference} = 331 - 300 = \text{Rs. } 31 \]
Using the three-year formula \( P\left[\left(1+\tfrac{R}{100}\right)^{3} - 1 - \tfrac{3R}{100}\right] = 1000(1.331 - 1.3) \) gives the same Rs. 31 in one step.
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