# Present Value of a Perpetuity Calculator

LAST UPDATE: September 29th, 2019

### What is a Present Value (PV) of a Perpetuity?

The present value (PV) of a perpetuity is the value in today’s dollars of a series of payments that has no end. It uses a payment amount and rate of return to calculate the value of the payments in today’s dollars.

Compared with the present value of an annuity (which has the payment occur for a set number of periods), a perpetuity has payments continue forever (theoretically).

### Present Value of a Perpetuity Formula – How the PV of a Perpetuity is calculated

$\text{Present Value} = \frac{\text{Payment Amount}}{\text{Interest Rate}}$

Where:

• Payment” is the payment each period.
• Rate of Return” is a decimal rate of return per period (the calculator above uses a percentage). A return of 2.2% per period would be calculated in the formula as “0.022”.

### Example

We will receive a perpetuity of \$100 each year. The interest rate is 2.2% compounded annually. What is the present value of this perpetuity?
$\text{Present Value} = \frac{100}{0.022}$
$\text{Present Value} = 4545.45$

### What is the difference between the present value of an annuity and a perpetuity?

The present value of an annuity is for a set number of payments. A perpetuity is for an unlimited number of payments.

### What is the difference between a perpetuity and a growing perpetuity?

A perpetuity keeps the same payment through its entire existence. A growing perpetuity increases by a set amount each payment period.