## Future Value for Annuities

On occasion, it's also handy to know a shortcut for calculating the future value of an annuity. As you might guess, there are future value factors for annuities as well as present value factors. In general, the future value factor for an annuity is given by:

Annuity FV factor = (Future value factor - 1)/r

To see how we use annuity future value factors, suppose you plan to contribute \$2,000 every year to a retirement account paying 8 percent. If you retire in 30 years, how much will you have?

The number of years here, t, is 30, and the interest rate, r,is 8 percent, so we can calculate the annuity future value factor as:

Annuity FV factor = (Future value factor - 1)/r = (1.0830 - 1)/.08 = (10.0627 - 1)/.08 = 113.2832

The future value of this 30-year, \$2,000 annuity is thus:

Annuity future value = \$2,000 X 113.28 = \$226,566.40

Sometimes we need to find the unknown rate, r,in the context of an annuity future value. For example, if you had invested \$100 per month in stocks over the 25-year period ended December 1978, your investment would have grown to \$76,374. This period

Ross et al.: Fundamentals of Corporate Finance, Sixth Edition, Alternate Edition

III. Valuation of Future Cash Flows

6. Discounted Cash Flow Valuation