A trust wants to pay Rs. 1,500 at the end of every quarter for ever. If money is worth 10% per annum compounded quarterly, the amount the trust must invest now is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → Rs. 60,000
Payments that go on for ever form a perpetuity. The amount needed now is its present value; for a payment R at the end of each period and rate i per period,
\( \displaystyle P = \frac{R}{i} \)
The payments are quarterly, so the rate per quarter is
\( \displaystyle i = \frac{10\%}{4} = 2.5\% = 0.025 \)
With R = 1500:
\( \displaystyle P = \frac{1500}{0.025} = 60000 \)
So the trust must invest Rs. 60,000. Check: 2.5% of Rs. 60,000 is Rs. 1,500, exactly one quarterly payment.
Why the other options are incorrect
Option (1) Rs. 15,000 — Incorrect. This is 1500 ÷ 0.10, which uses the yearly rate with a quarterly payment.
Option (3) Rs. 61,500 — Incorrect. This is 1500 + 60000, the value when each payment is made at the beginning of the quarter; here the payments are at the end.
Option (4) Rs. 2,40,000 — Incorrect. This is 6000 ÷ 0.025, the yearly total of the payments divided by the quarterly rate.