1. Copyright © 2008 Pearson Education Canada11-1 Chapter 11 Ordinary Simple Annuities Contemporary Business Mathematics With Canadian Applications Eighth Edition S. A. Hummelbrunner/K. Suzanne Coombs PowerPoint: D. Johnston

2. Copyright © 2008 Pearson Education Canada11-2 Objectives After completing Chapter eleven, the student will be able to: Distinguish different types of annuities. Compute the future value(or accumulated value) FV for ordinary simple annuities. Compute the present value (or discounted value) PV for ordinary simple annuities. Compute the payment, number of periods, and interest rate for ordinary simple annuities.

3. Copyright © 2008 Pearson Education Canada11-3 What Is an Annuity?

4. Copyright © 2008 Pearson Education Canada11-4 Annuity Terminology payment interval - length of time between successive payments term of an annuity - length of time from the beginning of the first payment interval to the end of the last payment interval periodic rent - size of each regular payment annual rent - sum of periodic payments in one year

5. Copyright © 2008 Pearson Education Canada11-5 Types of Annuities Annuities certain -- fixed term Contingent annuities -- indefinite or uncertain term Perpetuity -- infinite number of payments

6. Copyright © 2008 Pearson Education Canada11-6 Examples of Annuities Certain The beginning and ending dates are known. Rental payments for real estate Lease payments on equipment Installment payments on loans Mortgage payments Interest payments on bonds and debentures

7. Copyright © 2008 Pearson Education Canada11-7 Examples of Contingent Annuities Beginning date or ending date or both are uncertain. Life insurance premiums Pension payments Payments from an RRSP converted into a life annuity Payments from a trust fund for the remaining life of a surviving spouse

8. Copyright © 2008 Pearson Education Canada11-8 Examples of Perpetuities Payments considered to continue forever. Size of periodic payment less than or equal to the periodic interest earned by a fund. Scholarship fund University endowment fund

9. Copyright © 2008 Pearson Education Canada11-9 Annuities Ordinary annuity -- Payments are made at the end of each payment period. Annuity due -- Payments are made at the beginning of each payment period. Deferred -- First payment is delayed for a specified time period or for a time period that may have to be calculated.

10. Copyright © 2008 Pearson Education Canada11-10 Annuities Simple annuity -- Interest conversion period is the same as the payment interval. General annuity -- Interest conversion period and payment interval are not the same.

11. Copyright © 2008 Pearson Education Canada11-11 Ordinary Simple Annuity Payments are made at the end of each payment interval.(i.e. Ordinary) Interest conversion period and payment interval are the same.(i.e. Simple)

12. Copyright © 2008 Pearson Education Canada11-12 Example of Simple Ordinary Annuity The interest rate is 6% compounded annually

13. Copyright © 2008 Pearson Education Canada11-13 Future Value of an Annuity Rate-6% compounded annually Annual payments

14. Copyright © 2008 Pearson Education Canada11-14 Future Value Formula

15. Copyright © 2008 Pearson Education Canada11-15 Formula for Finding the Future Value of an Annuity

16. Copyright © 2008 Pearson Education Canada11-16 Compounding or Accumulation Factor

17. Copyright © 2008 Pearson Education Canada11-17 Future Value of Annuity

18. Copyright © 2008 Pearson Education Canada11-18 Present Value of Annuity The formula for finding the present value of an annuity is derived by finding the sum of a geometric progression. The geometric progression is made up of the present values of the individual payments in the cash flow.

19. Copyright © 2008 Pearson Education Canada11-19 Present Value Formula

20. Copyright © 2008 Pearson Education Canada11-20 Discounting Factor for Present Value Equation

21. Copyright © 2008 Pearson Education Canada11-21 Example of PV 6% compounded annually Annual year-end payments of $100

22. Copyright © 2008 Pearson Education Canada11-22 Finding PV Using the Formula

23. Copyright © 2008 Pearson Education Canada11-23 Present Value Application

24. Copyright © 2008 Pearson Education Canada11-24 Finding Cash Value

25. Copyright © 2008 Pearson Education Canada11-25 Electronic Calculator Solution for PV of Mortgage Payments

26. Copyright © 2008 Pearson Education Canada11-26 Home purchased for $100,000 Assume a rate of 8% compounded semi- annually with monthly payments over 25 years.

27. Copyright © 2008 Pearson Education Canada11-27 Summary