Thus far we have dealt with single payments, or “lump sums.” However, many assets provide a series of cash inflows over time, and many obligations like auto, student, and mortgage loans require a series of payments. If the payments are equal and are made at fixed intervals, then the series is an annuity. For example,$100 paid at the end of each of the next three years is a three-year annuity. If the payments occur at the end of each year, then we have an ordinary (or deferred) annuity. If the payments are made at the beginning of each year, then we have an annuity due. Ordinary annuities are more common in finance, so when we use the term “annuity” in this book, assume that the payments occur at the ends of the periods unless otherwise noted.
Here are the time lines for a $100, three-year, 5 percent, ordinary annuity and for the same annuity on an annuity due basis. With the annuity due, each payment is shifted back to the left by one year. A $100 deposit will be made each year, so we show the payments with minus signs:
As we demonstrate in the following sections, we can find an annuity’s future and present values, the interest rate built into annuity contracts, and how long it takes to reach a financial goal using an annuity. Keep in mind that annuities must have constant payments and a fixed number of periods. If these conditions
don’t hold, then we don’t have an annuity.
What’s the difference between an ordinary annuity and an annuity due?
Why should you rather receive an annuity due for $10,000 per year for 10 years than an otherwise similar ordinary annuity?
