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Perpetuity

Definition

An infinite series of equal payments. A growing perpetuity increases at a constant rate.

How It Works

PV of a perpetuity = PMT / r. For a growing perpetuity, PV = PMT / (r - g) where g < r.

Formula

PV = PMT / r

Example

A $50 annual payment forever at 5% has PV = $50 / 0.05 = $1,000.

Common Misconceptions

✗Nothing lasts forever (British consols came close)
✗You can have g >= r (the formula breaks)

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FAQs

Common questions about Perpetuity

Terminal value calculations, preferred stock valuation, and some endowment models.

Because each successive payment is worth less in present value terms due to discounting. The sum of an infinite series of declining present values converges to PMT/r, which is a finite number as long as r > 0.