A firm anticipates an expenditure of Rs. 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 \((1.025)^{20}=1.7\)}
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → Rs. 357.14
The quarterly deposits R form an annuity whose future value must be Rs. 10,000. Per quarter:
\( \displaystyle i = \frac{10\%}{4} = 0.025,\quad n = 5\times 4 = 20 \)
By the sinking fund formula:
\( \displaystyle 10000 = R\times\frac{(1+i)^n - 1}{i} \)
\( \displaystyle = R\times\frac{1.7 - 1}{0.025} = 28R \)
\( \displaystyle R = \frac{10000}{28} \approx 357.14 \)
So the firm should deposit Rs. 357.14 every quarter.