Perpetuity Value Calculator
A perpetuity is a stream of equal payments that continues forever, and this calculator finds its present value: what an endless run of cash is worth in today's money. The idea seems odd at first, because the payments never stop, yet the value is finite. Each future payment is discounted back to the present, and the further away it lies the less it adds, so the sum converges on a single number. For a level perpetuity, the present value is simply the payment divided by the discount rate. If you expect the payments to grow at a steady rate each period, the growing perpetuity formula divides the payment by the discount rate minus the growth rate, which only works when the discount rate is larger. This tool handles both cases and guards against the situation where growth meets or beats the discount rate, since that has no finite answer. Perpetuities appear in real finance: they value preferred shares with fixed dividends and form the terminal value step of a discounted cash flow valuation. Every figure here is computed deterministically from the standard formula, and the worked example below reconciles exactly to the calculator's default inputs so you can trace each step yourself.
A level perpetuity is worth PV = payment / discount rate. A $1,000 annual payment discounted at 5% is worth $20,000.00 today. A growing perpetuity uses payment divided by (rate minus growth).
Perpetuity value formula
Level perpetuity: PV = PMT / r
Growing perpetuity: PV = PMT / (r - g), valid only when r > g
PMT = payment per period
r = discount rate per period (as a decimal)
g = growth rate per period (as a decimal)
For a level perpetuity, dividing the payment by the discount rate captures the full sum of an infinite, equally weighted but ever-shrinking series. For a growing perpetuity, the gap between the discount rate and the growth rate replaces the plain discount rate. When the growth rate equals or exceeds the discount rate, the series does not converge and the calculator returns a guidance message instead of a number.
Worked example
A preferred share pays 1,000 every year, with no growth, and your required return is 5% per year. Because the growth rate is zero, this is a level perpetuity.
- Convert the discount rate to a decimal: 5% = 0.05
- Growth rate is 0, so use the level formula PV = PMT / r
- PV = 1,000 / 0.05
- PV = 20,000.00
The present value is 20,000.00. These are the calculator's default inputs, so the result above matches the widget exactly.
Present value of a 1,000 level perpetuity at common rates
For a level perpetuity, present value is the payment divided by the discount rate.
| Discount rate | Present value of 1,000 per period |
|---|---|
| 3% | 33,333.33 |
| 4% | 25,000.00 |
| 5% | 20,000.00 |
| 8% | 12,500.00 |
| 10% | 10,000.00 |
Time value of money concepts: US Securities and Exchange Commission, Investor.gov.
Perpetuity value calculator: frequently asked questions
What is a perpetuity?
A perpetuity is a stream of equal cash payments that continues forever, with no end date. Classic examples include certain government bonds known historically as consols and some preferred shares that pay a fixed dividend indefinitely. Although the payments never stop, the present value is finite because each future payment is worth steadily less once discounted back to today.
How is the present value of a perpetuity calculated?
For a level perpetuity, present value equals the payment divided by the discount rate: PV = PMT / r. For a growing perpetuity, where each payment rises by a fixed rate g, present value equals PMT divided by the rate minus the growth: PV = PMT / (r - g). The growing version only gives a finite, meaningful answer when the discount rate is greater than the growth rate.
Why must the discount rate exceed the growth rate?
If the growth rate equals or exceeds the discount rate, the payments grow at least as fast as they are discounted, so the present value does not converge to a finite number. The formula PMT / (r - g) would divide by zero or a negative number, which has no economic meaning. This calculator guards against that case and shows a message rather than a misleading figure.
Where are perpetuities used in practice?
The perpetuity formula appears in the terminal value step of a discounted cash flow valuation, where future cash flows beyond the forecast period are treated as a growing perpetuity. It also values preferred stock with a fixed dividend and helps price level annuities that are long enough to approximate a perpetuity. It is a building block of the wider time value of money toolkit.
What is the difference between a perpetuity and an annuity?
An annuity pays a fixed amount for a set number of periods, then stops. A perpetuity pays forever. Because a perpetuity has no end, its present value formula is simpler than an annuity's: you divide the payment by the discount rate, with no term to track. An annuity's present value is always lower than an otherwise identical perpetuity.
Official sources
- Time value of money, present value and investing basics: US Securities and Exchange Commission, Investor.gov. As at 24 June 2026.
Reviewed by the CalculatorHub team, edited by James Graham, 24 June 2026. See our methodology. This is general information, not financial, tax, legal or investment advice.