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Perpetuity Calculator

Quick answer

PV = PMT ÷ r: a 2,000 annual payment forever at 8% is worth 25,000 today; growing at 2%, the Gordon value is 2,000 ÷ (0.08 − 0.02) = 33,333.

Figures are estimates from this calculator’s standard formula — adjust the inputs in the tool below for your exact number.

How Does the Perpetuity Calculator Work?

PV = PMT ÷ r | Growing: PV = PMT₁ ÷ (r − g)

A perpetuity pays a fixed amount forever with no maturity. Its value is the payment divided by the discount rate — the simplest valuation in finance and the base of the Gordon growth model. The computation rests on PV = PMT ÷ r | Growing: PV = PMT₁ ÷ (r − g). A 2,000 annual payment at an 8% discount rate is worth 2,000 ÷ 0.08 = 25,000; let it grow 2% a year and the value becomes 2,000 ÷ (0.08 − 0.02) = 33,333 — growth adds a third. Each input you type is substituted the instant you release the key, and the result is expressed in exactly the units or currency you chose.

  1. 1

    Step 1

    Start with the primary figures the Perpetuity Calculator asks for.

  2. 2

    Step 2

    Your values are substituted into PV = PMT ÷ r | Growing: PV = PMT₁ ÷ (r − g).

  3. 3

    Step 3

    Read off the computed result.

  4. 4

    Step 4

    Vary one input at a time to see its effect.

Use Cases

Endowment sizing

Computing the capital behind a perpetual scholarship

Preferred stock valuation

Pricing a fixed dividend with no redemption

Rental income approximation

Treating steady rent as a growing perpetuity

Gordon model check

Sanity-testing a DCF terminal value

Common Mistakes

  • Using nominal payments with real rates

  • Terminal value abuse

  • Forgetting taxes and fees

FAQs

Do perpetuities really exist?

Yes: UK consols paid for centuries, preferred stock has no maturity, and scholarship endowments mimic perpetuities by spending only their return.

Why must g be less than r?

If payments grew at or above the discount rate, the infinite sum diverges — no finite price could fund it.

What formula does the Perpetuity Calculator use?

It computes PV = PMT ÷ r | Growing: PV = PMT₁ ÷ (r − g) — with r is the discount rate and g the payment growth rate (must be below r).

Does it store the numbers I enter?

No — the Perpetuity Calculator computes locally in your browser, so nothing you type is saved or transmitted anywhere.

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