Enter the amount of the first payment, discount rate, and growth rate into the calculator to determine the present value of a growing perpetuity.

## Growing Perpetuity Formula

The following formula is used to calculate the present value of a growing perpetuity.

PV = D / (r - g)

Variables:

- PV is the present value of the growing perpetuity D is the amount of the first payment r is the discount rate g is the growth rate

To calculate the present value of a growing perpetuity, divide the amount of the first payment by the difference between the discount rate and the growth rate.

## What is a Growing Perpetuity?

A growing perpetuity is a series of periodic payments that grow at a proportionate rate and continue indefinitely. It is a type of perpetuity, which is an infinite series of payments. The concept is often used in finance to determine the present value of a company’s cash flows, dividends, or other financial metrics that are expected to grow at a constant rate over an indefinite period. The formula for calculating the present value of a growing perpetuity takes into account the initial payment, the growth rate, and the discount rate.

## How to Calculate Growing Perpetuity?

The following steps outline how to calculate the Present Value of a Growing Perpetuity.

- First, determine the amount of the first payment (D).
- Next, determine the discount rate (r).
- Next, determine the growth rate (g).
- Next, gather the formula from above = PV = D / (r – g).
- Finally, calculate the Present Value of the Growing Perpetuity.
- After inserting the variables and calculating the result, check your answer with a financial calculator or spreadsheet.

**Example Problem:**

Use the following variables as an example problem to test your knowledge.

Amount of the first payment (D) = $100

Discount rate (r) = 0.05

Growth rate (g) = 0.03