A charitable trust wants to pay Rs. 750 at the end of every month for ever to an old-age home. If money is worth 9% per annum compounded monthly, the amount the trust must invest now is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → Rs. 1,00,000
The present value of a perpetuity of R payable at the end of each period is \(\displaystyle\frac{R}{i}\), where i is the rate per period.
The payments are monthly, so the rate per month is
\( \displaystyle i = \frac{0.09}{12} = 0.0075 \)
So the amount to be invested now is
\( \displaystyle P = \frac{750}{0.0075} = 100000 \)
Why the other options are incorrect
Option (1) Rs. 8,333.33 — Incorrect. This is 750 ÷ 0.09, which uses the yearly rate with a monthly payment.
Option (2) Rs. 1,00,750 — Incorrect. This is the value when the first payment is made today; here every payment is at the end of the month.
Option (4) Rs. 9,000 — Incorrect. This is only one year of payments (750 × 12), not the value of payments that go on for ever.