The present value of a perpetuity of Rs. 5,000 payable at the beginning of each year, if the money is worth 8% effective is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → Rs. 67,500
A perpetuity payable at the beginning of each period is a perpetuity due. Its present value is the first payment (made now) plus the present value of an ordinary perpetuity:
\( \displaystyle PV=R+\frac{R}{i}=5000+\frac{5000}{0.08} \)
\( \displaystyle PV=5000+62500=67500 \)
So the present value is Rs. 67,500.
Why the other options are incorrect
Option (2) Rs. 76,500 — Incorrect. The present value is 5,000 + 62,500 = Rs. 67,500, not Rs. 76,500.
Option (3) Rs. 56,500 — Incorrect. Rs. 56,500 is less than even the ordinary perpetuity value of Rs. 62,500, so it cannot be the value of a perpetuity due.
Option (4) Rs. 62,500 — Incorrect. Rs. 62,500 = 5000/0.08 is the present value when payments are made at the end of each year (ordinary perpetuity); it leaves out the payment made at the beginning.
CBSE Applied Mathematics (Class XII):
Perpetuity
