What sum of money is needed to invest now, so as to get Rs. 5000 at the beginning of every month forever, if the money is worth 6% per annum compounded monthly?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → Rs. 10,05,000
Payments made forever form a perpetuity. Since each payment is made at the beginning of the month, it is a perpetuity due: the first payment is made at once, and the rest form an ordinary perpetuity.
\( \displaystyle i = \frac{6}{12 \times 100} = 0.005 \)
\( \displaystyle P = R + \frac{R}{i} \)
\( \displaystyle = 5000 + \frac{5000}{0.005} \)
\(= 5000 + 1000000 = 1005000\)
So the sum needed is Rs. 10,05,000.
Why the other options are incorrect
Option (1) Rs. 10,00,500 — Incorrect. The value is \(1000000 + 5000 = 1005000\), not 1000500.
Option (2) Rs. 10,50,000 — Incorrect. The value is \(1000000 + 5000 = 1005000\), not 1050000.
Option (3) Rs. 10,00,000 — Incorrect. This is \(\frac{R}{i}\) alone, the value when payments are made at the end of each month. Here they start at once, so one more payment of Rs. 5000 is needed.
CBSE Applied Mathematics (Class XII):
Perpetuity
