A company establishes a sinking fund to provide for payment of Rs. 2,50,000 debt, maturing in 4 years. Contributions to the fund are to be made at the end of each year. Find the amount of each annual deposit if interest rate is 18% p.a. [Assume \((1.18)^4 \approx 2\)]
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → Rs. 45,000
Let each annual deposit be Rs. R. The deposits form an ordinary annuity, and in a sinking fund its amount after 4 years must equal the debt:
\( \displaystyle S = R\left[\frac{(1+i)^n - 1}{i}\right] \)
\( \displaystyle 250000 = R\left[\frac{(1.18)^4 - 1}{0.18}\right] \)
\( \displaystyle 250000 = R\left[\frac{2 - 1}{0.18}\right] = \frac{R}{0.18} \)
\( R = 250000 \times 0.18 = 45000 \)
So each annual deposit is Rs. 45,000.
CBSE Applied Mathematics (Class XII):
Sinking Fund
