A man invests ₹ 4000 for 3 years at compound interest. After one year the money amounts to ₹ 4320. What will be the amount (to the nearest rupee) due at the end of 3 years? (R.R.B., 2006)

### Concept & Formula The amount under compound interest is calculated using the formula: $$A = P \left(1 + \frac{R}{100}\right)^n$$ When the amount after 1 year is given, we can directly find the rate of interest, which remains constant for subsequent years. ### Step-by-Step Solution * Given Principal $P = 4000$ * Amount after 1 year $A_1 = 4320$ * Interest for the first year $= 4320 - 4000 = 320$ * Rate $R = \left(\frac{\text{Interest} \times 100}{P \times 1}\right) = \frac{320 \times 100}{4000} = 8\%$ p.a. * Now, find the amount due at the end of 3 years using $R = 8\%$ and $n = 3$: $A_3 = 4000 \times \left(1 + \frac{8}{100}\right)^3$ $A_3 = 4000 \times (1.08)^3$ * Calculate $(1.08)^3$: $1.08 \times 1.08 = 1.1664$ $1.1664 \times 1.08 = 1.259712$ * $A_3 = 4000 \times 1.259712 = 5038.848$ * Rounding to the nearest rupee gives ₹ 5039. ### Exam Strategy & Shortcut Instead of recalculating from the base $P = 4000$ for 3 years, you can treat the amount after 1 year ($4320$) as the principal for the remaining 2 years: $4320 \times (1.08)^2 = 4320 \times 1.1664 = 5038.848$. This saves one multiplication step. ### Common Pitfall A frequent mistake is applying the interest for 3 years simply as simple interest ($320 \times 3 = 960 \implies 4960$), completely ignoring the compounding effect on the interest itself. ### Final Answer Therefore, the correct answer is **₹ 5039**.