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

Answer: (C)

₹357.14

Answer 2

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.