What is the present value formula for a perpetuity paying PMT indefinitely?

• A. PV = PMT / r
• B. PV = PMT × r
• C. PV = PMT × (1 + r)
• D. PV = PMT × [1 - (1 + r)^-n]

Answer: (A)

A perpetuity delivers a fixed payment each period forever, so its present value is the sum of all those payments discounted back to today. If the payment is PMT each period and the discount rate per period is r, the value today equals PMT divided by r.

Think of the present value as an infinite geometric series: PMT/(1+r) + PMT/(1+r)^2 + PMT/(1+r)^3 + ... . The sum of this infinite series is PMT/r, which is why the present value formula for a perpetuity is PMT divided by r.

This relies on constant payments, payments occurring at the end of each period, and a positive discount rate. The other expressions relate to different setups: finite annuities (D) and other forms that don’t match the perpetuity case.