**Future value of growing annuity = P [{ (1 + r)**^{n}** – (1 + g)**^{n}** } ÷ (r – g) ]**

P = first payment

r = rate

g = rate

n = # of periods

Future value of the growing annuity is utilized to determinethe amount received at the end of an investment with a series of cash flowswhich grows at a constant rate. This type of investment is also known as a perpetuity.Another name of a growing annuity is also known as increasing annuity.

## How the future value of growing annuity induced

The present value of growing annuity formula can be used todetermine the future value of growing annuity;

Present value of growing annuity = [P ÷ (r – g)] × [1 – {(1+ g) ÷ (1 + r)}^{n} ]

Now we can convert the present value in the above formula tothe future value. For that, we multiply ** (1 + r)^{n}** and in result,the equation will become;

= [P ÷ (r – g)] × [(1 + r)^{n} – (1 + g)^{n}]

The next step is to factor out the ** P** from the above equation which will then result in the same formula as we listed at top of this page.

### Future value of growing annuity examples

Let’s suppose that a person plans to invest in a savingsaccount with his one month salary ($2700 per month salary). The savings accountwill grow the money at a rate of 6% per annum. Salary increases with an averageof 7% per year, so each year the savings amount will also increaserespectively. We will not assume any taxes, increments or any other adjustmentsto the salary to make things simple for basic understanding. Now calculate theending balance after 8 years by using future value of growing annuity formulaat the top of this page.

In the above example, the growth rate for investment will be7%, the initial cash flow will be $2,700. The rate per period will be 6% andthe number of periods will be 8 years. Now putting all the given data in theformula to get;

FV of growing annuity = $2,700 [{(1 + 0.06)^{8} – (1+ 0.07)^{8}} ÷ {0.06 – 0.07}]

FV of growing annuity = $35,100

The account balance after 8 years will be $35,100 in thesavings account.