## Future Value of an Ordinary Annuity and Annuity Due Future Value of an Ordinary Annuity

The future value of an ordinary annuity involves payments (receipts) of an equal sum of money at the end of each period for a certain number of periods and allows the interest to accumulate over the total period of time. For example, a deposit of \$1,000 made at the end of every year for five years earning 6 percent will grow to \$5,637.10, as shown in Table 9.1.

TABLE 9.1 Future value of ordinary annuity of \$1,000 compounded at 6% for 5 years

1,060.00

In Table 9.1 the future value of an ordinary annuity is found by compounding each deposit and summing the interest earned on the deposits. This annuity can also be expressed in equation form as follows:

FV = 1,000(1+ 0.06)4 + 1,000(1+ 0.06)3 + 1,000(1+ 0.06)2 + 1,000(1 + 0.06) +1,000

= 1,262.48 + 1,191.02 + 1,123.60 + 1,060.00 + 1,000

This calculation can be cumbersome if you don't have a calculator or if the time period is long. Financial tables can simplify the calculation, as shown in Worksheet 9.1 using the same example. The future value of an ordinary annuity table is shown in Appendix C.

WORKSHEET 9.1 How to determine the future value of an ordinary annuity using financial tables

Where

PMT = Annuity or regular payment/receipt FVIFA = Future value interest factor of an annuity i = Interest rate per period n = Number of periods

Example:

FV = PMT (FVIFA i, n) FV = 1,000 (FVIFA 6%, 5) FV = 1,000 (5.637) FV = \$5,637

### Step 1 Fill in the values.

Step 2 Fill in the FVIFA factor from Appendix C at intersection of i row and n column. Step 3 Multiply the annuity by the interest factor to obtain the future value. 