Future Value of Growing Annuity

The formula for the future value of a growing annuity is used to calculate the future amount of a series of cash flows, or payments, that grow at a proportionate rate. A growing annuity may sometimes be referred to as an increasing annuity.

Example of FV of Growing Annuity

An example of the future value of a growing annuity formula would be an individual who is paid biweekly and decides to save one of her extra paychecks per year. One of her net paychecks amounts to $2,000 for the first year and she expects to receive a 5% raise on her net pay every year. For this example, we will use 5% on her net pay and not involve taxes and other adjustments in order to hold all other things constant. In an account that has a yield of 3% per year, she would like to calculate her savings balance after 5 years.

The growth rate in this example would be the 5% increase per year, the initial cash flow or payment would be $2,000, the number of periods would be 5 years, and rate per period would be 3%. Using these variables in the future value of growing annuity formula would show

After solving this equation, the amount after the 5th cash flow would be $11,700.75.

How is the FV of Growing Annuity Derived?

The future value of a growing annuity formula can be found by first looking at the following present value of a growing annuity formula

Present Value can be converted into future value by multiplying the present value times(1+r)ⁿ. By multiplying the 2nd portion of the PV of growing annuity formula above by(1+r)ⁿ, the formula would show as

From here, the formula above is the same as the formula shown at the top of the page after factoring out the initial payment, P.