Present Value (PV) of a growing perpetuity (Gordon Growth Model) calculator

Present Value of a Growing Perpetuity Calculator

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

Present value (PV) of an annuity is a financial calculation used when determining the “today” value of an set of annuity payments that regularly grow and 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 Growing Perpetuity calculated?

The PV of a growing perpetuity is calculated through the Gordon Growth Model, a financial formula used with the time value of money.
\text{Present Value} = \frac{\text{Payment Amount}}{\text{Interest Rate} - \text{Payment Growth Rate}}


We will receive a perpetuity of $100 each year. The interest rate at the moment is 2.2% compounded annually. The payment grows by 0.5% each compounding period. What is the present value of this perpetuity?
\text{Present Value} = \frac{-100}{0.022 - 0.005}
\text{Present Value} = \frac{-100}{0.017}
\text{Present Value} = -5882.35

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A payment is an amount either deposited or withdrawn at each compounding period. A negative number designates an amount that is deposited, while a positive one withdrawn.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'.

What is the Payment Growth Amount?

The payment growth amount is the amount that the payment grows each compounding period.