Question

A firm anticipates an expenditure of ₹10,000 for a new equipment at the end of 5 years from now. How much should the firm deposit at the end of each quarter into a sinking fund earning interest 10% per year compounded quarterly to provide for the purchase?
[Use (1.025)²⁰=1.7]

• A. ₹368.55
• B. ₹298.40
• C. ₹357.14
• D. ₹745.03

Answer 1

The Correct Option is C

The formula for sinking fund payments is:

\(A = \frac{S}{\left(1 + r\right)^n - 1} \cdot \frac{r}{r}\)

where \(A\) is the periodic payment, \(S\) is the future value (target amount), \(r\) is the interest rate per period, and \(n\) is the total number of periods.

Here:

\(S = 10,000, \quad r = 0.025 \, (\text{quarterly interest rate}), \quad n = 20 \, (\text{quarters}).\)

The sinking fund factor is:

\(\frac{\left(1.025\right)^{20} - 1}{0.025} = \frac{1.7 - 1}{0.025} = \frac{0.7}{0.025} = 28.\)

The quarterly deposit is:

\(A = \frac{10,000}{28} = 357.14.\)

Thus, the firm should deposit Rs. 357.14 at the end of each quarter.