Mr. Jayesh plans to save amount for higher studies of his daughter, required after 10 years. How much amount should he save at the beginning of each year to accumulate Rs. 1,00,000 at the end of 10 years, if rate of interest is 12% compounded annually? [Given \((1.12)^{11} = 3.5\)]
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → Rs. 5042
Payments at the beginning of each year form an annuity due. Each payment earns interest for one period more than in an ordinary annuity, so its amount after n years is
\( \displaystyle S = R(1 + i)\,\frac{(1 + i)^n - 1}{i} = R\,\frac{(1 + i)^{n+1} - (1 + i)}{i} \)
With i = 0.12 and n = 10, the given value \((1.12)^{11} = 3.5\) can be used directly:
\( \displaystyle 100000 = R \times \frac{3.5 - 1.12}{0.12} = R \times \frac{2.38}{0.12} \)
\( \displaystyle R = \frac{100000 \times 0.12}{2.38} = \frac{12000}{2.38} \approx 5042 \)
So he should save about Rs. 5042 at the beginning of each year.