A man invests Rs. 5000 for 3 years at 5% per annum 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 in his account at the end of the third year.

Introduction / Context: This question combines compound interest with tax deducted on interest each year. The tax reduces the effective rate of growth of the investment. We must compute the net amount the investor has at the end of 3 years after accounting for both compounding and yearly tax deductions.

Given Data / Assumptions:

• Principal P = Rs. 5000.
• Nominal rate of interest r = 5% per annum.
• Time t = 3 years.
• Interest is compounded yearly.
• Income tax is charged at 20% on the interest earned each year.
• Tax is deducted at the end of each year before the next year's interest is calculated.

Concept / Approach:

Each year, gross interest is P_current * 5%. However, only 80% of this interest is actually credited to the account because 20% is taken away as tax. Thus the effective interest rate credited to the investor is 5% * 80% = 4% per year. We can therefore treat the situation as if the principal earns compound interest at an effective rate of 4% per annum for 3 years.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

The other figures do not correspond to a consistent 5% gross rate with 20% tax on the interest. They either assume the full 5% interest without tax or use an incorrect effective rate. Only Rs. 5624.32 matches the detailed year by year calculation.

Common Pitfalls:

A typical error is to calculate compound interest at 5% for 3 years and then subtract tax on the total interest, instead of taxing each year's interest separately. Another pitfall is to confuse the tax rate on interest with a tax rate on the principal.

Final Answer:

The amount at the end of the third year is Rs. 5624.32.