To determine the quarterly deposit (\( R \)) for a sinking fund, the objective is to accumulate ₹10,000 over 5 years with a 10% annual interest rate compounded quarterly. The future value (FV) of a sinking fund is calculated using the formula:
\[ FV = R \times \frac{(1 + i)^n - 1}{i} \]
The parameters are:
- \( FV = 10,000 \)
- \( i = \frac{0.10}{4} = 0.025 \)
- \( n = 5 \times 4 = 20 \)
Given \((1.025)^{20} = 1.7\), the equation becomes:
\[ 10,000 = R \times \frac{1.7 - 1}{0.025} \]
Simplifying the equation:
\[ 10,000 = R \times \frac{0.7}{0.025} \]
\[ 10,000 = R \times 28 \]
Solving for \( R \):
\[ R = \frac{10,000}{28} \approx 357.14 \]
Consequently, the firm must deposit ₹357.14 each quarter.
The required deposit is ₹357.14.