Perpetuity Calculator
A perpetuity is the infinite cousin of an annuity. Instead of valuing ten payments, 120 payments, or a 20-year withdrawal period, it values a payment stream that is modeled as continuing without an end date. That sounds unrealistic at first, but the math is useful because distant cash flows are discounted so heavily that the total can still be finite. Preferred stock dividends, long-lived royalties, ground rents, endowment spending rules, and terminal value estimates are common finance examples.
This calculator is different from the finite present value of annuity calculator. The annuity calculator stops after a chosen number of periods; the perpetuity calculator assumes the stream continues indefinitely. It is also different from the future value of annuity calculator, which grows deposits forward, and from the annuity payout calculator, which solves for income from a lump sum over a finite term. For a general annuity overview, start with the annuity calculator.
What the calculator does
The form asks for a dividend or payment, a discount rate, and a growth rate. The calculation requires a nonnegative payment, a positive discount rate, a nonnegative growth rate, and a growth rate below the discount rate. If those conditions are not met, the result is invalid because the perpetuity formula would not produce a finite planning value.
The calculator subtracts the growth rate from the discount rate to get the spread. It then divides the payment by that spread expressed as a decimal. It also shows what the value would be with no growth, using the payment divided by the discount rate. That comparison makes the growth assumption visible instead of hiding it inside one large value.
Formula
For a level perpetuity, the present value is:
For a growing perpetuity, the present value is:
Here, PMT is the periodic payment, r is the discount rate as a decimal, and g is the growth rate as a decimal. The form accepts rates as percentages, so 8% is entered as 8, not 0.08. The rates and the payment must describe the same interval. If the payment is annual, use annual discount and growth rates. If the payment is monthly, use monthly rates.
Worked example matching the default inputs
The default inputs are a $10 payment, an 8% discount rate, and a 2% growth rate. The spread is 8% minus 2%, or 6%. Expressed as a decimal, the spread is 0.06. The growing perpetuity value is therefore $10 divided by 0.06, which equals $166.67.
The calculator also reports the no-growth value. With the same $10 payment and an 8% discount rate, a level perpetuity is worth $10 divided by 0.08, or $125.00. The gap between $166.67 and $125.00 is the value of assuming the payment grows at 2% forever. That is a powerful assumption, so it deserves close scrutiny.
If the growth rate were changed to zero, the primary label would become level perpetuity value and the result would match the no-growth line. If growth were raised to 8% or more, the calculator would reject the input because the discount-less-growth spread would be zero or negative.
Why an infinite stream has finite value
A perpetuity does not imply that infinite dollars today are being created. Present value discounts future cash. A payment due next period matters a lot. A payment due centuries from now is discounted by so many periods that its contribution is tiny. When the discount rate is positive and growth is below that discount rate, the discounted values form a converging series.
That is why the spread is so important. A small spread creates a high valuation because growth almost offsets the discount rate. A large spread creates a lower valuation because future payments shrink quickly in present-value terms. Moving the default growth rate from 2% to 3% changes the denominator from 6% to 5%, raising the value from $166.67 to $200.00.
Perpetuity versus insurance annuity
In everyday finance, annuity often means an insurance contract. Perpetuity is usually a valuation model. A life annuity can pay for as long as a person lives, but it is priced with mortality assumptions and insurer expenses, not by assuming payments literally last forever for everyone. A perpetuity model ignores those insurance features and focuses only on cash-flow timing, discounting, and growth.
For investment analysis, the same caution applies. A preferred stock dividend may be intended to continue, but the issuer can face credit stress. A royalty can decline if the underlying asset weakens. A terminal value can dominate a valuation model if the growth rate is set too close to the discount rate. The formula is simple; the assumptions are not.
Tips for using the result
- Keep the payment and rates on the same schedule. Annual payments need annual rates; quarterly payments need quarterly rates.
- Treat the growth rate as a long-run sustainable assumption, not as a short-term forecast.
- Check the no-growth value to see how much of the result comes from the growth assumption.
- Avoid tiny spreads unless you have a strong reason. A discount rate of 7% and growth of 6.5% produces a very large value because the denominator is only 0.5%.
- Use finite annuity tools when the payment stream has a known end date.
Informational note
This calculator is educational and does not determine fair value for a security, insurance product, pension, or business. Real decisions should consider credit risk, liquidity, taxes, fees, contract rights, and the possibility that payments or growth assumptions change.
Formula sources and scope
- Principles of Finance — OpenStax, Rice University (peer-reviewed open textbook); 2022 first edition, ISBN 978-1-951693-54-1; Jurisdiction-neutral finance definitions. Supports: level perpetuity PV=C/r; growing perpetuity PV=C/(r-g), requiring r>g. Accessed 2026-07-09.
These sources support the stated formula or definition. Results remain estimates based on the entered values and do not replace financial, legal, tax, lending, or investment advice. Compare periods, units, accounting definitions, and jurisdiction-specific rules before acting.