Question

The present value of a sequence of payments of ₹ 100 made at the end of every year and continuing forever, if the money is worth 5% compounded annually, is

• A. ₹ 2,000
• B. ₹ 20,000
• C. ₹ 5,000
• D. ₹ 12,000

Hint:

For perpetuities, use the simple formula $P = \frac{A}{r}$—it's valid when payments continue forever and rate stays constant.

Answer 1

The Correct Option is C

This is a problem of perpetuity — a series of identical payments continuing indefinitely.
The present value $P$ of a perpetuity is given by $P = \frac{A}{r}$, where:
$A$ is the annual payment (₹100), and $r$ is the annual interest rate (5% or 0.05).
So, $P = \frac{100}{0.05} = ₹2,000$
Therefore, the present value of the perpetuity is ₹2,000.