A trust has Rs. 1,10,000 and wants to award a prize of Rs. 9,000 at the end of every year for ever. If money is worth 6% per annum compounded annually, how much more must the trust add to its fund now?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → Rs. 40,000
The fund needed is the present value of a perpetuity of Rs. 9,000 paid at the end of each year:
\( \displaystyle P = \frac{R}{i} = \frac{9000}{0.06} = 150000 \)
The trust already has Rs. 1,10,000, so it must add
\( 150000 - 110000 = 40000 \)
Why the other options are incorrect
Option (1) Rs. 1,50,000 — Incorrect. This is the whole fund needed; the Rs. 1,10,000 already held must be taken away.
Option (2) Rs. 49,000 — Incorrect. This uses 1,59,000, the fund needed when the first prize is given today; here every prize is at the end of the year.
Option (4) Rs. 2,400 — Incorrect. This is the yearly shortfall in income (9,000 − 6,600), not the sum to be added now.