# Present Value of a Perpetuity Calculator

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

Present value (PV) of an annuity is a financial calculation used when determining the “today” value of an set of annuity payments that occur each compounding period that go on forever.
As this calculator is structured to parallel the results of a financial calculator, inputs and outputs will be similar – for example, a negative present value (or payment) means an outflow as opposed to a directly negative number.

### How is the Present Value of a Perpetuity calculated?

The PV of a perpetuity is calculated through a financial formula used with the time value of money.
$text{Present Value} = frac{text{Payment Amount}}{text{Interest Rate}}$

### Example

We will receive a perpetuity of \$100 each year. The interest rate at the moment 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 rate?

The rate is the amount of interest earned per compounding period.

### What is Payment (PMT)?

A payment is an amount either deposited or withdrawn at each compounding period. A negative number designates an amount that is deposited, while a positive one withdrawn. For example, if \$100 is deposited each compounding period, it would be entered as '-100', while if \$75 was payed out each compounding period, it would be entered as '75'.