Ajesh has set up a sinking fund in order to have Rs. 10,00,000 after 10 years for his son's education. The amount should be set aside at the end of every 6 months into an account paying 5% per annum compounded half yearly is: [given \((1.025)^{20} = 1.6386\)]
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → Rs. 39,148.1
A sinking fund with equal deposits R at the end of each period grows like an ordinary annuity:
\( \displaystyle A = R\left[\frac{(1 + i)^n - 1}{i}\right] \)
Here the rate per half-year and the number of half-years are
\( \displaystyle i = \frac{5\%}{2} = 0.025,\quad n = 10 \times 2 = 20 \)
So
\( \displaystyle 1000000 = R\left[\frac{1.6386 - 1}{0.025}\right] \)
\( \displaystyle R = \frac{1000000 \times 0.025}{0.6386} \)
\( \displaystyle = \frac{25000}{0.6386} \approx 39148.1 \)
So Rs. 39,148.1 should be set aside every 6 months.