A temple trust wants to pay Rs. 21,000 for repairs at the end of every 2 years for ever. If money is worth 10% per annum compounded annually, the present value of these payments is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → Rs. 1,00,000
Here one payment period is 2 years, so the rate must be the rate for a two-year period. Rs. 1 grows in 2 years to
\( (1.1)^2 = 1.21 \)
so the rate per two-year period is
\( j = 1.21 - 1 = 0.21 \)
The present value of the perpetuity is
\( \displaystyle P = \frac{R}{j} = \frac{21000}{0.21} = 100000 \)
Why the other options are incorrect
Option (2) Rs. 1,05,000 — Incorrect. This uses 0.20 (twice 10%) as the two-year rate; with yearly compounding the two-year rate is 0.21.
Option (3) Rs. 2,10,000 — Incorrect. This uses the yearly rate 0.10, as if Rs. 21,000 were paid every year.
Option (4) Rs. 1,21,000 — Incorrect. This adds one more payment of Rs. 21,000, as if the first payment were made today.