At what rate of interest will the present value of a perpetuity of Rs. 1000, payable at the end of every quarter be Rs. 20000 :
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 20% per annum
The present value of a perpetuity of R per period at rate i per period is
\( \displaystyle P = \frac{R}{i} \)
Here the period is a quarter, R = 1000 and P = 20000:
\( \displaystyle 20000 = \frac{1000}{i} \)
\(i = 0.05 = 5\% \text{ per quarter}\)
A year has 4 quarters, so the annual rate (compounded quarterly) is
\(4 \times 5\% = 20\% \text{ per annum}\)
Why the other options are incorrect
Option (1) 10% per annum — Incorrect. This gives 2.5% per quarter and a present value of 1000 ÷ 0.025 = Rs. 40000.
Option (3) 3% per quarter — Incorrect. The present value would be 1000 ÷ 0.03 ≈ Rs. 33333.33.
Option (4) 10% per quarter — Incorrect. The present value would be 1000 ÷ 0.10 = Rs. 10000.