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:
(Use \((1.05)^{10} \approx 1.6\))
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → Rs. 72,000
Deposits of R = 12,000 at the end of each year for n = 10 years at i = 0.05 build up to the amount of an annuity:
\( \displaystyle A = R\,\frac{(1+i)^{n}-1}{i} \)
\( \displaystyle = 12000 \times \frac{(1.05)^{10}-1}{0.05} \)
\( \displaystyle = 12000 \times \frac{1.6-1}{0.05} \)
\(= 12000 \times 12 = 144000\)
The fund holds Rs. 1,44,000 after 10 years. The bond needs Rs. 72,000, so the surplus is
\(144000 - 72000 = 72000\)