A firm anticipates an expenditure of Rs. 5,00,000 for plant modernization at the end of 10 years from now, then the amount the company should deposit at the end of each year into a sinking fund earning interest 5% per annum is [use \( (1.05)^{10}=1.629 \)]
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → Rs. 39,745.63
The yearly deposits R must build up to S = Rs. 5,00,000 in 10 years at i = 0.05. By the sinking fund (amount of an annuity) formula:
\( \displaystyle S=R\left[\frac{(1+i)^n-1}{i}\right] \)
\( \displaystyle 500000=R\times\frac{1.629-1}{0.05} \)
\( \displaystyle R=\frac{500000\times 0.05}{0.629} \)
\( \displaystyle =\frac{25000}{0.629} \)
\( \displaystyle \approx 39745.63 \)
So the company should deposit Rs. 39,745.63 each year.