There is 60% increase in an amount in 6 years at simple interest. What will be the compound interest of ₹ 12,000 after 3 years at the same rate?

### Concept & Formula Rate of Simple Interest: $$R = \frac{SI \times 100}{P \times T}$$ Compound Interest formula: $$CI = P \left[\left(1 + \frac{R}{100}\right)^T - 1\right]$$ ### Step-by-Step Solution 1. **Find the Rate of Interest ($R$):** * Let the original sum be $P = 100$. * Increase in 6 years ($SI$) = 60. $$R = \frac{60 \times 100}{100 \times 6} = 10\% \text{ per annum}$$ 2. **Calculate Compound Interest for 3 years:** * $P = \text{₹ } 12000$, $R = 10\%$, $T = 3\text{ years}$ $$A = 12000 \times \left(1 + \frac{10}{100}\right)^3 = 12000 \times \left(\frac{11}{10}\right)^3$$ $$A = 12000 \times \frac{1331}{1000} = 12 \times 1331 = \text{₹ } 15972$$ $$CI = A - P = 15972 - 12000 = \text{₹ } 3972$$ ### Exam Strategy & Shortcut For $R = 10\%$ over 3 years, the effective compound interest rate is $33.1\%$. $$CI = 33.1\% \text{ of } 12000 = 33.1 \times 120 = \text{₹ } 3972$$ ### Common Pitfall Confusing the 6-year period from the first part of the problem with the 3-year period required for calculating compound interest. ### Final Answer Therefore, the correct answer is **₹ 3972**.