### More Articles

- How to Compute Annuity if Given the Rate & Number of Years
- What Are the Differences Between a Future Annuity & the Present Value of an Annuity?
- Equation for the Present Value of Preferred Stock
- How to Calculate the Value of Reinvested Dividends Using Excel
- What Is the Difference Between Book Value & Market Value Per Share of Common Stock?
- How to Calculate the Value of Stock With the Price-to-Earnings Ratio

A growing annuity is a series of increasing, periodic cash flows that grow at a fixed percentage. For example, you might deposit money into an account each year for five years. If each deposit is 5 percent greater than the last, the series of deposits is a growing annuity. The future value of the growing annuity is the accumulated value of the payments at the end of the last payment period. The present value is the value of the payments in today’s dollars. If you know the future value, you can use two growing annuity formulas to calculate the present value.

Substitute the future value of the growing annuity into the formula FV/[((1 + R)^N - (1 + G)^N)/(R - G)], in which FV represents future value, R represents the interest rate per period, G represents the payment growth rate per period and N represents the number of payment periods. For example, assume a five-year growing annuity has a 6 percent annual interest rate, a future value of $250,000 and payments that grow 2 percent per year. The formula is $250,000/[((1 + 0.06)^5 - (1 + 0.02)^5)/(0.06 - 0.02)].

Step 2Calculate the numbers in each set of parentheses. In this example, add 1 to 0.06 to get 1.06. Add 1 to 0.02 to get 1.02. Subtract 0.02 from 0.06 to get 0.04. This leaves $250,000/[(1.06^5 - 1.02^5)/(0.04)].

Step 3Calculate the numbers in brackets. In this example, raise 1.06 to the fifth power to get 1.3382. Raise 1.02 to the fifth power to get 1.1041. Subtract 1.1041 from 1.3382 to get 0.2341. Divide 0.2341 by 0.04 to get 5.8525. This leaves $250,000/5.8525.

Step 4Divide the remaining numbers to calculate the growing annuity’s first payment. In this example, divide $250,000 by 5.8525 to get an initial payment of $42,717.

Step 5Plug the initial payment and other variables into the formula [P/(R - G)] x [1 - ((1 + G)/(1 + R))^N], in which P represents the initial payment. The other variables are the same as the previous formula. Continuing the example, the formula is [$42,717/(0.06 - 0.02)] x [1 - ((1 + 0.02)/(1 + 0.06))^5].

Step 6Solve the numbers in the first set of brackets. In this example, subtract 0.02 from 0.06 to get 0.04. Divide $42,717 by 0.04 to get $1,067,925. This leaves $1,067,925 x [1 - ((1 + 0.02)/(1 + 0.06))^5].

Step 7Calculate the numbers in the remaining brackets. In this example, add 1 to 0.02 to get 1.02. Add 1 to 0.06 to get 1.06. Divide 1.02 by 1.06 to get 0.9623. Raise 0.9623 to the fifth power to get 0.8252. Subtract 0.8252 from 1 to get 0.1748. This leaves $1,067,925 x 0.1748.

Step 8Multiply the remaining numbers to calculate the present value of the growing annuity. Concluding the example, multiply $1,067,925 by 0.1748 to get a present value of $186,673. This means the value of the growing payment stream is worth $186,673 today.