# Future Value of a Growing Annuity Calculator

## What does it do?

This future value of a growing annuity calculator works out the future value (FV) of a regular sum of money (Pmt) which is growing or declining at a constant rate (g) each period. Additionally it is assumed the payments are made at the end of each period for n periods, and a discount rate i is applied.

## Future Value of a Growing Annuity Calculator Formula

The future value of a growing annuity formula is shown below.

`FV = Pmt x ( (1 + i)n - (1 + g)n ) / (i - g)`

The calculator uses this formula to compute the future value (FV) by entering details relating to the regular payment (Pmt), growth rate (g), discount rate (i) and the number of periods (n). The Excel annuity calculator is available for download below.

## Future Value of a Growing Annuity Calculator Instructions

The calculator is used as follows.

Step 1 (Pmt)

Firstly enter the regular payment amount (Pmt). The regular payment is the amount received at the end of each period for n periods. It is important to realize that the amount must be the same for each period.

Step 2 (g)

Secondly enter the growth rate (g). The growth rate is the rate at which the original payment (Pmt) is growing each period. The rate should be for a period. For example, if the period is a year, then the rate should be the yearly growth rate.

Step 3 (i)

Next enter the discount rate (i). The discount rate is the rate used to discount each payment amount back from the end of the period in which is was made, to the beginning of period 1 (today). The rate should be for a period. For example, if the period is a year, then the rate should be the yearly rate.

Step 4 (n)

Finally enter the number of periods (n). The number of periods is entered. A period can be any term (month, year etc), but must be consistent with the discount rate (i) provided.

Step 5

The future value of a growing annuity calculator works out the future value (FV). It is important to realize that the answer is the value at the end of period n of an a regular sum of money growing at a constant rate (g) each period, received at the end of each of the n periods, and discounted at a rate of i. It is the future value of a growing annuity.