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 1
The correct answer is Option (1) → Rs. 10,05,000
Payments made forever form a perpetuity; here they come at the beginning of each month, so it is a perpetuity due. The monthly rate is
\( \displaystyle i = \frac{6}{12 \times 100} = 0.005 \)
The first payment is made at once, and the remaining payments form an ordinary perpetuity worth \(\frac{R}{i}\):
\( \displaystyle P = R + \frac{R}{i} \)
\( \displaystyle = 5000 + \frac{5000}{0.005} \)
\(= 5000 + 1000000 = 1005000\)
So the sum needed is Rs. 10,05,000.
CBSE Applied Mathematics (Class XII):
Perpetuity
