# How to Calculate the Present Value of a Growing Annuity Using the Future Value

by Ryan Menezes

A fixed annuity pays the policy holder set payments over the course of its life. A growing annuity's payments, however, increase over time, making the policy similar to other growing investments. Each future payment is worth less to you now that an equivalent amount of cash. If you had cash rather than the promise of future money, you could invest it, netting you even more money by the time the annuity paid out. A discount rate equivalent to the U.S. Treasury borrowing rate derives the net present value of future earnings.

1. Add 1 to the annuity's growth rate and discount rate. For example, if an annuity offers a growth rate of 4 percent and the discount rate is 6 percent: 1 + 0.04 = 1.04; 1 + 0.06 = 1.06.

2. Divide the growth rate by the discount rate. In this example, 1.04 ÷ 1.06 = 0.981.

3. Raise the result to the power of the number of years until the annuity's payment. For this example, if you are calculating the present value of payments across 4 years: 0.981^4 = 0.926.

4. Subtract this answer from 1. In this example, 1 - 0.926 = 0.074.

5. Divide this answer by the difference between the discount and growth rates: 0.074 ÷ (0.06 - 0.04) = 3.7.

6. Multiply this answer by the future value of the annuity's first payment. If the first payment is \$10,000: 3.7 × \$10,000 = \$37,000. This is the present value of the growing annuity's payments.

#### References

• "Financial Mathematics"; Budi Frensidy; 2008
• "Quantitative Methods for Finance and Investments"; John L. Teall and Iftekhar Hasan; 2002

#### Resources

• "Financial Management"; Carlos Correia; 2007
• "Fundamentals of Corporate Finance"; Peter Moles, et. al.; 2002