Perpetuity Calculator — Present Value of Infinite Payments
Calculate the present value of a perpetuity — a stream of equal (or growing) payments that continue forever. Enter the annual payment, discount rate, and optional growth rate to see what the stream is worth today.
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Fair value of this perpetuity today: PV = C / (r − g)
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Discount rate
5% ÷ 100 = 0.05 - 2
Present value
1,000 ÷ 0.05 = 20,000PV = C ÷ r for a flat perpetuity.
How does this calculator work?
A perpetuity's present value is PV = C/r (flat) or PV = C/(r−g) (growing, g < r). At a 5% discount rate a €1,000/year flat perpetuity is worth €20,000 today; at 2% growth it becomes €1,000/(0.05−0.02) = €33,333. The raw break-even horizon (years of undiscounted payments to match PV) is 1/r for a flat perpetuity.
Formula
How this is calculated
A perpetuity promises a recurring payment C forever. Because a dollar received in the future is worth less than a dollar today — due to the opportunity cost of capital — each payment is discounted: the first is worth C/(1+r), the second C/(1+r)², and so on. Summing this infinite geometric series yields the closed-form PV = C/r for a flat perpetuity, where r is the annual discount rate expressed as a decimal.
A growing perpetuity increases its payment by a fixed annual rate g. The series sums to PV = C/(r−g) — the Gordon Growth Model used in dividend discount stock valuation — valid only when g < r. If g ≥ r, the present value would be infinite. The "payment multiple" PV/C shows how many single payments the present value equals; for a 5% flat perpetuity this is 20, meaning the PV equals 20 years of payments in today's money.
The calculator also shows the raw break-even horizon: the number of years of undiscounted cash flows needed to accumulate to PV. For a flat perpetuity this is simply 1/r years (20 years at 5%). The AreaCurve shows cumulative raw payments over 60 years — most of the total eventually paid lies far in the future and is heavily discounted, which is why PV is far less than the infinite sum of nominal payments.
Frequently asked questions
An annuity makes a fixed number of payments (e.g., 30 years). A perpetuity continues forever. The annuity PV formula converges to PV = C/r as the number of periods approaches infinity, making the perpetuity formula the upper bound for any finite annuity with the same payment and rate.
The formula PV = D/(r−g) is the classic dividend discount model for valuing a stock that pays a steadily growing dividend D at required return r and long-run growth g. It is a rough guide — it breaks down when g is close to r or growth is uneven.
Real financial instruments do not literally last forever. But the perpetuity formula is an accurate approximation when the payment stream is very long or open-ended, because at any positive discount rate the present value of payments beyond 40–50 years is negligibly small.
Also known as
TG we-Calculate Editorial Team. (2026). Perpetuity Calculator — Present Value of Infinite Payments [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/perpetuity-calculator
TG we-Calculate Editorial Team. "Perpetuity Calculator — Present Value of Infinite Payments." TG we-Calculate. 2026. https://we-calculate.com/calculator/perpetuity-calculator.
TG we-Calculate Editorial Team, "Perpetuity Calculator — Present Value of Infinite Payments," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/perpetuity-calculator
@misc{wecalculate_perpetuity_calculator, title = {Perpetuity Calculator — Present Value of Infinite Payments}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/perpetuity-calculator}}, year = {2026}, note = {TG we-Calculate} }
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