Ms. Sheela creates a fund of Rs. 1,00,000 for providing scholarships to needy children. The scholarship is provided in the beginning of the year. This fund earns an interest of r % per annum. If the scholarship amount is taken as Rs. 8,000, then r =
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(8\displaystyle\frac{16}{23}\)%
The scholarship of R = 8,000 is paid every year without end, at the beginning of each year. So the fund is the present value of a perpetuity due, with i = r/100:
\( \displaystyle P = R + \frac{R}{i} \)
\( \displaystyle 100000 = 8000 + \frac{8000}{i} \)
\( \displaystyle \frac{8000}{i} = 92000 \)
\( \displaystyle i = \frac{8000}{92000} = \frac{2}{23} \)
As a percentage:
\( \displaystyle r = \frac{200}{23} = 8\frac{16}{23}\,\% \)
Tip: Payment at the beginning of each year makes it a perpetuity due, P = R + R/i. With the ordinary perpetuity P = R/i the rate would be exactly 8%, which is not among the options.