A hostel wants to pay Rs. 2,500 to a mess fund at the beginning of every six months for ever, the first payment being made today. If money is worth 10% per annum compounded half-yearly, the sum the hostel needs today is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → Rs. 52,500
Since the first payment is made today, the sum needed is the first payment plus a perpetuity of the later payments.
The period is six months, so the rate per period is
\( \displaystyle i = \frac{0.10}{2} = 0.05 \)
\( \displaystyle P = R + \frac{R}{i} \)
\( \displaystyle P = 2500 + \frac{2500}{0.05} \)
\( P = 2500 + 50000 = 52500 \)
Why the other options are incorrect
Option (1) Rs. 50,000 — Incorrect. This leaves out the payment made today.
Option (2) Rs. 27,500 — Incorrect. This divides by the yearly rate 0.10; the payments are half-yearly, so the half-yearly rate 0.05 must be used.
Option (4) Rs. 47,500 — Incorrect. This subtracts the payment made today instead of adding it.