A person has set up a sinking fund in order to have Rs. 20,000 in 10 years for his children’s education. The amount to set aside each quarter into an account paying 6% per annum compounded quarterly is: (use \( (1.015)^{40}=1.8140 \))
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → Rs. 368.55
A sinking fund is built by equal payments R at the end of each period, so its value after n periods is the amount of an ordinary annuity:
\( \displaystyle A=R\left[\frac{(1+i)^n-1}{i}\right] \)
Payments are quarterly, so the rate per quarter is \( i=\frac{6\%}{4}=0.015 \) and the number of quarters is \( n=10\times 4=40 \).
\( \displaystyle 20000=R\left[\frac{(1.015)^{40}-1}{0.015}\right] \)
\( \displaystyle 20000=R\left[\frac{1.8140-1}{0.015}\right] \)
\( \displaystyle 20000=R\cdot\frac{0.8140}{0.015} \)
\( \displaystyle R=\frac{20000\times 0.015}{0.8140} \)
\( \displaystyle =\frac{300}{0.8140} \)
\( \displaystyle \approx 368.55 \)
So Rs. 368.55 must be set aside each quarter.