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Ordinary Annuity
An ordinary annuity pays out at the end of the time interval. Most annuities fall into this category.
Consider the following two examples representing annuities that require payments of $500 per
period over 10 periods.
For the ordinary annuity, we have the simple payment schedule shown in Exhibit 4.9.
Exhibit 4.9 Payments into an ordinary annuity.
Exhibit 4.10 Payments into an annuity due.
Annuity Due
An annuity due is one that pays at the beginning of the time interval. A good example of an annuity
due would be paying into a savings account.
For the annuity due, we have the simple payment schedule shown in Exhibit 4.10.
Note that we have not considered the interest rate in the two examples, but confirm that these are
annuities since they meet the three criteria: They (1) pay an equal amount, (2) at a specific time
interval, (3) for a specific time period. Note also that each payment is a negative amount; this reflects
payments made. As previously mentioned, the negative sign (indicated by parentheses) is important
when using financial calculators, or Excel to solve for the present and future values of annuities.
Calculating the Future Value of an Ordinary Annuity
If we make payments into an annuity under the preceding two payment schedules, Exhibits 4.9 and
4.10, the FV of the annuity due will be higher than the FV of the ordinary annuity. The reason for this
is that the first annuity due payment is made in period 0; therefore, it will begin to earn interest one
period earlier than the ordinary annuity.