A man invests ₹ 5000 for 3 years at 5% p.a. compound interest reckoned yearly. Income tax at the rate of 20% on the interest earned is deducted at the end of each year. Find the amount at the end of the third year. (M.A.T., 2004)

### Concept & Strategy When income tax is deducted on the interest earned each year, it effectively reduces the rate of interest. If $20\%$ of the interest goes to tax, the investor keeps $80\%$ of the interest. Effective Rate of Interest $= \text{Nominal Rate} \times (1 - \text{Tax Rate})$. ### Step-by-Step Solution * Nominal Rate $= 5\%$ p.a. * Tax Rate on interest $= 20\%$ * The effective rate of interest the man earns is $80\%$ of $5\%$. Effective Rate $= 5\% \times \left(\frac{100 - 20}{100}\right) = 5 \times 0.8 = 4\%$ * Now, calculate the compound interest amount with $P = 5000$, $R = 4\%$, and $n = 3$ years: Amount $A = P \times \left(1 + \frac{R}{100}\right)^n$ $A = 5000 \times \left(1 + \frac{4}{100}\right)^3$ $A = 5000 \times (1.04)^3$ * Calculate $(1.04)^3$: $1.04^2 = 1.0816$ $1.0816 \times 1.04 = 1.124864$ * $A = 5000 \times 1.124864 = 5624.32$ ### Exam Strategy & Shortcut By finding the effective interest rate upfront ($4\%$), you transform a complex taxation problem into a standard, straightforward compound interest calculation. ### Common Pitfall Calculating the interest year by year, deducting $20\%$, and adding it to the principal for three iterations is extremely tedious and prone to calculation errors. Always find the effective rate first. ### Final Answer Therefore, the correct answer is **₹ 5624.32**.