1. Copyright © Cengage Learning. All rights reserved. 5 MATHEMATICS OF FINANCE

2. Copyright © Cengage Learning. All rights reserved. 5.2 Annuities

3. 3 Future Value of an Annuity

4. 4 An annuity is a sequence of payments made at regular time intervals. The time period in which these payments are made is called the term of the annuity. Depending on whether the term is given by a fixed time interval, a time interval that begins at a definite date but extends indefinitely, or one that is not fixed in advance, an annuity is called an annuity certain, a perpetuity, or a contingent annuity, respectively.

5. 5 Future Value of an Annuity In general, the payments in an annuity need not be equal, but in many important applications they are equal. Annuities are also classified by payment dates. An annuity in which the payments are made at the end of each payment period is called an ordinary annuity, whereas an annuity in which the payments are made at the beginning of each period is called an annuity due. Furthermore, an annuity in which the payment period coincides with the interest conversion period is called a simple annuity, whereas an annuity in which the payment period differs from the interest conversion period is called a complex annuity.

6. 6 Future Value of an Annuity In other words, we study annuities that are subject to the following conditions: 1. The terms are given by fixed time intervals. 2. The periodic payments are equal in size. 3. The payments are made at the end of the payment periods. 4. The payment periods coincide with the interest conversion periods.

7. 7 Future Value of an Annuity (9)

8. 8 Future Value of an Annuity

9. 9 Example 1

10. 10 Example 1 – Solution  1268.25 or $1268.25. Use a calculator. cont’d

11. 11 Practice p. 291 Self-Check Exercises #1