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 firm needs to calculate the quarterly deposit, \( R \), required to accumulate ₹10,000 in a sinking fund earning 10% interest compounded quarterly over 5 years. The formula for the future value of a sinking fund is:

\[ FV = R \times \frac{(1 + i)^n - 1}{i} \]

Where:

• \( FV = 10,000 \) (future value)
• \( i = \frac{0.10}{4} = 0.025 \) (quarterly interest rate)
• \( n = 5 \times 4 = 20 \) (total number of quarters)

Using the given \((1.025)^{20} = 1.7\), substitute into the formula:

\[ 10,000 = R \times \frac{1.7 - 1}{0.025} \]

Simplify:

\[ 10,000 = R \times \frac{0.7}{0.025} \]

\[ 10,000 = R \times 28 \]

Solve for \( R \):

\[ R = \frac{10,000}{28} \approx 357.14 \]

Therefore, the firm should deposit ₹357.14 at the end of each quarter.

The correct option is: ₹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.