Question

A multinational company creates a sinking fund by setting a sum of Rs. 12,000 annually for 10 years to pay off a bond issue of Rs. 72,000. If the fund accumulates at\(5\% \)per annum compound interest, then the surplus after paying for bond is

• A. Rs. 78,900
• B. Rs. 68,500
• C. Rs. 72,000
• D. Rs. 1,44,000

Answer 1

The Correct Option is C

The accumulated value of the sinking fund is calculated using the formula:

\[ A = P \cdot \frac{(1 + r)^n - 1}{r}. \]

Here:

- \( P = 12,000 \),

- \( r = 0.05 \),

- \( n = 10 \),

- \( (1.05)^{10} \approx 1.6 \).

Substitute into the formula:

\[ A = 12,000 \cdot \frac{1.6 - 1}{0.05} = 12,000 \cdot \frac{0.6}{0.05} = 12,000 \cdot 12 = 1,44,000. \]

The surplus is:

\[ \text{Surplus} = A - 72,000 = 1,44,000 - 72,000 = Rs.72,000. \]