## Formula

FV = Pmt x ( (1 + i)^{n}- (1 + g)^{n}) / (i - g)

**Variables used in the annuity formula**

FV = Future Value

Pmt = Periodic payment

i = Discount rate

g = Growth rate

n = Number of periods

## Use

The future value of growing annuity formula shows the value at the end of period n of series of periodic payments which are growing or declining at a constant rate (g) each period. The payments are made at the end of each period for n periods, and a discount rate i is applied.

A growing annuity is sometimes referred to as an increasing annuity or graduated annuity.

The formula compounds the value of each payment forward to its value at the end of period n (future value).

## Example Using the Future Value of a Growing Annuity Formula

If a payment of 8,000 is received at the end of period 1 and grows at a rate of 6% for each subsequent period for a total of 10 periods, and the discount rate is 3%, then the value of the payments at the end of period 10 is given by the future value of a growing annuity formula as follows:

FV = Pmt x ( (1 + i)^{n}- (1 + g)^{n}) / (i - g) FV = 8,000 x ( (1 + 3%)^{10}- (1 + 6%)^{10}) / (3% - 6%) FV = 119,181.68

## Discount Rate Equals Growth Rate

In the special case where the discount rate (i), is equal to the growth rate (g), the formula above cannot be used as the term (i – g) goes to zero.

In this situation the following formula is used.

FV = Pmt x n x (1 + i)^{(n-1)}

The future value of a growing annuity formula is one of many annuity formulas used in time value of money calculations, discover another at the links below.

## About the Author

Chartered accountant Michael Brown is the founder and CEO of Double Entry Bookkeeping. He has worked as an accountant and consultant for more than 25 years in all types of industries. He has been the CFO or controller of both small and medium sized companies and has run small businesses of his own. He has been a manager and an auditor with Deloitte, a big 4 accountancy firm, and holds a BSc from Loughborough University.