A man invests Rs 5000 for 3 years at 5% per annum compound interest, reckoned yearly. Income tax at the rate of 20% is deducted from the interest earned at the end of each year. What is the amount in his account at the end of the third year?

Introduction:
This question combines compound interest with taxation on interest income. Each year the man earns interest at 5% on the current balance, but 20% of that interest is taken away as income tax. Only the remaining 80% of the interest is added to his account, which effectively reduces the growth rate of his investment.

Given Data / Assumptions:

• Initial investment (principal) = Rs 5000.
• Nominal rate of interest = 5% per annum.
• Interest is calculated and credited yearly (compounded annually).
• Income tax rate on interest = 20% of the interest earned each year.
• Time period = 3 years.
• Tax is deducted each year before adding net interest to the principal.

Concept / Approach:
Each year, the gross interest is 5% of the current amount. Income tax of 20% is charged on this interest, so only 80% of the computed interest is actually added. That means the effective annual increase is 5% * (1 − 0.20) = 4% of the principal. Therefore, the effective annual growth factor for the amount is 1.04, not 1.05. We can treat this as compound interest at an effective rate of 4% per annum for 3 years.

Step-by-Step Solution:
Effective net interest rate per year = 5% * 80% = 5% * 0.8 = 4%.So each year the amount is multiplied by 1.04.Initial amount A0 = Rs 5000.Amount after 3 years: A3 = 5000 * (1.04)^3.Compute (1.04)^2 = 1.0816.Then (1.04)^3 = 1.0816 * 1.04 = 1.124864.Therefore A3 = 5000 * 1.124864 = Rs 5624.32.

Verification / Alternative Check:
You can verify year by year. Year 1: interest = 5000 * 5% = 250, tax = 20% of 250 = 50, net interest = 200, new amount = 5200. Year 2: interest = 5200 * 5% = 260, tax = 52, net interest = 208, amount = 5408. Year 3: interest = 5408 * 5% = 270.40, tax = 54.08, net interest = 216.32, final amount = 5408 + 216.32 = 5624.32. This matches the effective 4% compounding method.

Why Other Options Are Wrong:
Rs 5423 and Rs 5500: These underestimate the growth, likely arising from misapplying the tax or simple interest calculations.Rs 5634 and Rs 5976: These overestimate the final amount, possibly by ignoring tax in some years or by using the full 5% rate as if no tax were deducted.

Common Pitfalls:
Many learners forget that tax is deducted each year and not just at the end of the full term, which changes the effective rate. Some simply compute compound interest at 5% for 3 years and then subtract one year’s tax, which is incorrect. Always adjust the rate first or handle each year's interest and tax sequentially for accurate results.

Final Answer:
The amount in the man's account at the end of 3 years, after deducting income tax on interest each year, is Rs 5624.32.