A perpetuity sounds infinite, but its value is finite because distant payments are worth very little today. At 5%, $1,000 a year forever is worth $20,000. Growth makes it much more valuable – and very sensitive to the gap between r and g.
How to use the Perpetuity Calculator
- Payment per period
- Discount rate per period
- Growth rate per period
- First payment
Results update as you type, and every field accepts the units shown in its menu.
How it works
Enter the payment per period, the discount rate and the growth rate, and choose whether payments start now or after one period.
Tips
- Use the nominal annual rate and pick the compounding frequency your bank or broker states.
- Small differences in return or fees compound into large differences over decades.
- Run the calculation with a cautious, a central and an optimistic return to see the range of outcomes.
- Past returns do not guarantee future returns – nothing here is investment advice.
Common mistakes to avoid
- Comparing an APR with an APY or effective rate.
- Ignoring inflation, taxes and fees when judging a real return.
- Entering a percentage as a decimal (5 instead of 0.05 is correct here).
Inputs explained
| Field | What to enter |
|---|---|
| Payment per period | Amount in your currency |
| Discount rate per period | In % |
| Growth rate per period | In % |
| First payment | Choose one: After one period (ordinary), Today (perpetuity due) |
Example values
How the main result changes when Payment per period changes and everything else stays at the example values above:
| Payment per period | Present value of the perpetuity |
|---|---|
| 500 | 10,000 |
| 750 | 15,000 |
| 1,000 | 20,000 |
| 1,250 | 25,000 |
| 1,500 | 30,000 |
| 2,000 | 40,000 |
Formula
PV of a perpetuity = payment ÷ discount rateGrowing perpetuity: PV = next payment ÷ (r − g), r > gPerpetuity due: PV × (1 + r)Worked example
Inputs — Payment per period: $1,000; Discount rate per period: 5 %; Growth rate per period: 0 %; First payment: After one period (ordinary).
Results — Present value of the perpetuity = $20,000.00; Value as a multiple of the payment = 20 ×.
Frequently asked questions
What is a perpetuity?
A series of payments that continues forever.
How do I value a growing perpetuity?
Divide the next payment by (discount rate − growth rate).
What if growth exceeds the discount rate?
The value would be infinite – the formula doesn't apply.
What formula does the Perpetuity Calculator use?
PV of a perpetuity = payment ÷ discount rate.