The present value of a perpetuity of Rs. 7500 payable at the end of each year, if money is worth 5% compounded annually is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → Rs. 1,50,000
For a perpetuity paid at the end of each year, the present value is \( P=\frac{R}{i} \), with R = 7500 and i = 0.05:
\( \displaystyle P=\frac{7500}{0.05} \)
\( \displaystyle =150000 \)
So the present value is Rs. 1,50,000.
Why the other options are incorrect
Option (1) Rs. 1,57,500 — Incorrect. This is \( R+\frac{R}{i} \), the formula for payments at the beginning of each year.
Option (2) Rs. 95,000 — Incorrect. The present value is Rs. 1,50,000, not Rs. 95,000.
Option (4) Rs. 1,75,000 — Incorrect. The present value is Rs. 1,50,000, not Rs. 1,75,000.