About the Perpetuity Calculator
This perpetuity calculator finds the present value of a stream of payments that continues forever. Enter the payment, the discount rate and an optional growth rate, choose whether the first payment arrives now or at the end of the first period, and it returns the perpetuity’s value along with how much of that value comes from the first 30 periods and how long it takes to accumulate half of it.
Perpetuities appear throughout finance: preferred shares and consols that pay a fixed amount indefinitely, the Gordon growth model for valuing a stock from its dividends, the terminal value in a discounted cash flow (DCF) model, endowments and scholarships that must pay out forever, and ground rents. Students use the formula constantly in corporate finance courses.
The discount rate and growth rate must use the same period as the payment — annual payments with annual rates, for example. A growing perpetuity only has a finite value when the discount rate is higher than the growth rate; if growth matches or exceeds the discount rate the value is infinite.
With the default inputs, the present value of the perpetuity is $20,000.00. Change any value above to recalculate instantly.
How to use the perpetuity calculator
- 1Enter the payment per period — the first payment if it grows.
- 2Enter the discount rate (your required return) for the same period.
- 3Add a growth rate for a growing perpetuity, or leave it at 0.
- 4Choose whether the first payment arrives today or at the end of the period.
- 5Read the present value and see how much comes from the first N payments.
Formula and method
A level perpetuity paying C at the end of every period is worth C ÷ r: the infinite sum of discounted payments C/(1 + r) + C/(1 + r)² + … converges to that value. If payments grow at rate g each period, the first payment C is divided by the spread between the discount and growth rates, r − g, which is the Gordon growth model. A perpetuity due pays the first amount immediately, so its value is the ordinary value times (1 + r).
The share of value from the first n payments is 1 − ((1 + g) ÷ (1 + r))ⁿ for both ordinary and due perpetuities. The calculator uses it to show how quickly value accumulates and how many periods it takes to collect half of it. All rates must match the payment period.
- PV
- Present value of the perpetuity
- C
- Payment per period (first payment if growing)
- r
- Discount rate per period
- g
- Growth rate of payments per period
- n
- Number of payments counted
Worked examples
$1,000 a year forever at 5%
A level perpetuity is worth C ÷ r = $1,000 ÷ 0.05 = $20,000. The first 30 payments account for $15,372 of that (76.9%), and it takes 15 years of payments to accumulate half the value.
Gordon growth: $2.50 dividend growing 3%, 8% required return
Next year’s $2.50 dividend divided by the 5-point spread between the 8% required return and 3% growth gives a value of $50 per share. About 76% of that value comes from the next 30 years of dividends.
Endowment paying $5,000 today, growing 2%, at 4%
A growing perpetuity due is worth C × (1 + r) ÷ (r − g) = 5,000 × 1.04 ÷ 0.02 = $260,000. Because growth is close to the discount rate, only 44% of the value comes from the first 30 payments and half takes 36 years.
Frequently asked questions
What is the formula for a perpetuity?+
The present value of a perpetuity is PV = C ÷ r, where C is the payment each period and r is the discount rate per period. For payments that grow at rate g, use PV = C ÷ (r − g), where C is the first payment.
What is a perpetuity due?+
A perpetuity due makes its first payment immediately rather than at the end of the first period. Its value is the ordinary perpetuity value multiplied by (1 + r), or equivalently the ordinary value plus one payment for a level perpetuity.
Why must the discount rate exceed the growth rate?+
If payments grow as fast as or faster than the discount rate, each discounted payment is as large as or larger than the last, so the infinite sum never converges and the value is infinite. In practice long-run growth cannot exceed the economy’s growth indefinitely.
Where are perpetuities used in real life?+
Perpetuity formulas value preferred stock with fixed dividends, British consols, endowments and scholarships, and the terminal value in DCF models. The growing perpetuity is the Gordon growth model used to value dividend-paying stocks.
How do I value a perpetuity with monthly payments?+
Use a monthly discount rate and monthly growth rate with the monthly payment. For example, $100 a month at a 6% annual rate uses r = 0.5% per month, giving a value of $100 ÷ 0.005 = $20,000.
Results are estimates for educational purposes and are not financial advice. Rates, fees and terms vary — confirm with your lender or a licensed advisor before making decisions.