A perpetuity’s present value collapses to a simple formula rather than requiring a sum over a fixed number of periods.
How it works
The annual payment divided by the discount rate gives the present value of a perpetuity — the same core relationship this site’s terminal-value calculator uses in its growing form.
What this does not include
This assumes a flat, non-growing payment — this site’s separate terminal-value and growing-annuity calculators handle a payment that increases at a constant rate over time instead.
How to use this calculator
- Enter the annual payment and discount rate.
A worked example
A perpetual payment of $5,000 per year at a 6% discount rate: present value = 5,000 ÷ 0.06 = $83,333.33.
What the variables mean
| Variable | Meaning |
|---|---|
| Payment | Fixed payment received each period, forever |
| Discount rate | Rate used to convert future payments into today’s value |
Edge cases worth knowing
A perpetuity with infinite payments still has a finite present value — the entire point of this calculation, since each future dollar is worth progressively less today, and the sum of that shrinking series converges.
A discount rate of zero makes the present value infinite, which has no practical meaning — the calculator declines to show a result for that case.
Frequently asked questions
What’s a real-world example of a perpetuity?
A traditional UK government bond called a “consol” was historically issued as a true perpetuity, paying interest indefinitely with no maturity date.
Why is the formula so simple compared to a regular annuity?
Because the payments continue infinitely, the mathematical series simplifies to payment divided by rate — the finite-period complexity of a regular annuity’s formula disappears entirely.
Can a perpetuity’s discount rate be zero?
No — a zero discount rate would make the present value infinite, since an endless stream of payments would never lose value through discounting.
