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

A perpetuity represents an indefinite series of identical payments.
The formula for the present value ($P$) of a perpetuity is $P = \frac{A}{r}$.
In this formula, $A$ signifies the annual payment (₹100), and $r$ denotes the annual interest rate (5% or 0.05).
Applying these values, we calculate $P = \frac{100}{0.05} = ₹2,000$.
Consequently, the present value of this perpetuity is ₹2,000.