The present value of a sequence of payment of Rs. 1500 made at the end of every 6 months and continuing forever, if money is worth 4% per annum compound semi-annually is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → Rs. 75,000
Payments continuing forever form a perpetuity, whose present value is \( \frac{R}{i} \), where i is the rate per payment period.
Payments are half-yearly, so the rate per period is
\( \displaystyle i=\frac{4\%}{2}=2\%=0.02 \)
\( \displaystyle PV=\frac{R}{i}=\frac{1500}{0.02}=75000 \)
So the present value is Rs. 75,000.
Why the other options are incorrect
Option (1) Rs. 60,000 — Incorrect. The present value is \( \frac{1500}{0.02} \) = Rs. 75,000, not Rs. 60,000.
Option (2) Rs. 37,500 — Incorrect. Rs. 37,500 uses the annual rate 4% with the half-yearly payment, \( \frac{1500}{0.04} \); the rate must match the payment period.
Option (4) Rs. 76,500 — Incorrect. Rs. 76,500 adds one extra payment, 75,000 + 1,500, which is the value of a perpetuity whose first payment is made now (an annuity due), not at the end of the first period.
CBSE Applied Mathematics (Class XII):
Perpetuity
