Question

A person deposited a sum of 50,000 in a fixed deposit account which returns an annual interest of 10 percent compounded annually. However, an income tax of \(20\%\) is deducted on the interest amount at the end of each year. What would be the final value of the investment after 2 years?

• A. ₹ 58,000
• B. ₹ 58,320
• C. ₹ 59,400
• D. ₹ 60,500

Answer 1

The Correct Option is B

Compound Interest with Tax Deduction 

The given problem involves compound interest with annual tax deduction on the interest earned. The formula for compound interest is:

\[ A = P \left(1 + r_{\text{eff}}\right)^t \]

where:

• A is the final amount,
• P = 50,000 is the principal amount,
• r = 10% = 0.10 is the annual interest rate,
• t = 2 years is the time period,
• Tax Rate = 20% on interest.

Step 1: Compute Effective Interest Rate After Tax

The annual interest earned before tax:

\[ \text{Interest} = P \times r = 50,000 \times 0.10 = 5,000 \]

Tax on interest:

\[ \text{Tax} = 5,000 \times 0.20 = 1,000 \]

Net interest after tax:

\[ \text{Net Interest} = 5,000 - 1,000 = 4,000 \]

Effective interest rate after tax:

\[ r_{\text{eff}} = \frac{4,000}{50,000} = 0.08 \quad (8\%) \]

Step 2: Compute Final Amount After 2 Years

Using the effective interest rate in the compound interest formula:

\[ A = 50,000 \times (1.08)^2 \]

\[ A = 50,000 \times 1.1664 \]

\[ A = 58,320 \]

Final Answer:

Option (B) ₹58,320