Ramesh plans to save some amount required after 10 years for higher studies of his son. He expects the cost of these studies to be Rs.1,00,000. How much should he save at the beginning of each year to accumulate this amount at the end of 10 years, if the interest rate is 12% compounded annually. (Given \((1.12)^{11}=3.477\))
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → Rs. 5091
Payments at the beginning of each year form an annuity due. Each payment earns interest for one year more than in an ordinary annuity, so its amount after n years is
\( \displaystyle A = P\,\frac{(1 + i)^{n} - 1}{i}\,(1 + i) = P\,\frac{(1 + i)^{n+1} - (1 + i)}{i} \)
Here A = 1,00,000, i = 0.12 and n = 10. Using the given \((1.12)^{11} = 3.477\):
\( \displaystyle 100000 = P\,\frac{3.477 - 1.12}{0.12} \)
\( \displaystyle P = \frac{100000 \times 0.12}{2.357} = \frac{12000}{2.357} \)
\(P \approx 5091\)
So Ramesh should save about Rs. 5091 at the beginning of each year.
CBSE Applied Mathematics (Class XII):
Sinking Fund
