# Perpetuity Calculator

URL: https://speedycalculator.com/calculators/finance/perpetuity/
Last updated: 2026-10-25

> The perpetuity calculator works out the present value of a stream of equal (or steadily growing) payments that continues forever – used to value preferred stock, endowments and the terminal value of a business.

## Inputs

- Payment per period
- Discount rate per period (%)
- Growth rate per period (%)
- First payment

## Results

- Present value of the perpetuity
- Value as a multiple of the payment

## Formula

```
PV of a perpetuity = payment ÷ discount rate
Growing perpetuity: PV = next payment ÷ (r − g), r > g
Perpetuity due: PV × (1 + r)
```

## Explanation

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

FieldWhat to enterPayment per periodAmount in your currencyDiscount rate per periodIn %Growth rate per periodIn %First paymentChoose 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 periodPresent value of the perpetuity50010,00075015,0001,00020,0001,25025,0001,50030,0002,00040,000

## 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 ×.

## FAQ

**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.


## Sources

- [Corporate Finance Institute – financial ratios](https://corporatefinanceinstitute.com/)