Question

What sum of money should be deposited at the end of every 6 months to accumulate ₹ 50,000 in 8 years, if money is worth 6% p.a. compounded semi-annually?
\[ \text{{Given: }} (1.03)^{16} = 1.6047 \]

• A. ₹ 3,432.53
• B. ₹ 2,783.08
• C. ₹ 2,480.57
• D. ₹ 2,149.93

Hint:

For annuity calculations, use the compounded interest rate per period. Here, 6\% p.a. compounded semi-annually means \( r = 0.03 \) and the number of periods \( n = 16 \).

Answer 1

The Correct Option is C

Step 1: Use the formula for future value of annuity: \[ FV = R \cdot \frac{(1 + r)^n - 1}{r}. \] Rearrange to calculate \( R \): \[ R = \frac{FV \cdot r}{(1 + r)^n - 1}. \] Step 2: Substitute values: - \( FV = 50000 \), - \( r = \frac{6\%}{2} = 0.03 \), - \( n = 8 \times 2 = 16 \), - Given \( (1.03)^{16} = 1.6047 \). \[ R = \frac{50000 \times 0.03}{(1.03)^{16} - 1} = \frac{1500}{0.6047} \approx 2480.57. \]