2. Copyright © 2008 Pearson Education Canada Chapter 9 Compound Interest— Future Value and Present Value 9-1 Contemporary Business Mathematics With Canadian Applications Eighth Edition S. A. Hummelbrunner/K. Suzanne Coombs PowerPoint: D. Johnston

3. 9-2 Copyright © 2008 Pearson Education Canada Inc. Objectives After completing chapter nine, the student will be able to: Calculate interest rates and number of compounding periods Compute future (maturity) value. Compute the present value of future sums of money. Discount long-term promissory notes. Solve equivalent value problems.

4. 9-3 Copyright © 2008 Pearson Education Canada Inc. Compound Interest Interest for a specified time period is added to the original principal. The sum of the principal and interest becomes the new principal for the next time period. The amount of compound interest for the first period is the same as for simple interest but is greater for the following periods. 3

5. 9-4 Copyright © 2008 Pearson Education Canada Inc. Compounding of Interest Principal = 10000, Rate = 10% p.a. Term = 4 years

6. 9-5 Copyright © 2008 Pearson Education Canada Inc. Formula for Future Value

7. 9-6 Copyright © 2008 Pearson Education Canada Inc. Compounding Frequencies (determining periodic rate of interest)

8. 9-7 Copyright © 2008 Pearson Education Canada Inc. Determining Periodic Rate of Interest (i) i = j / m

9. 9-8 Copyright © 2008 Pearson Education Canada Inc. Finding Periodic Rate of Interest i= j/m Monthly8% = 0.66% 12

10. 9-9 Copyright © 2008 Pearson Education Canada Inc. Determining Compounding Factor (1+i) n

11. 9-10 Copyright © 2008 Pearson Education Canada Inc. Calculation of Future Value

12. 9-11 Simple Interest vs. Compound Interest

13. 9-12 Copyright © 2008 Pearson Education Canada Inc. Comparison of Simple and Compound Interest

14. 9-13 Copyright © 2008 Pearson Education Canada Inc. Future Value of an Investment FV = PV(1+i) n

15. 9-14 Copyright © 2008 Pearson Education Canada Inc. Finding FV When n Is a Fraction

16. 9-15 Copyright © 2008 Pearson Education Canada Inc. Computing Present Value (Discounting)

17. 9-16 Copyright © 2008 Pearson Education Canada Inc. Compound Discount (continued)

18. 9-17 Copyright © 2008 Pearson Education Canada Inc. Formula for Present Value

19. 9-18 Copyright © 2008 Pearson Education Canada Inc. Calculating Present Value

20. 9-19 Copyright © 2008 Pearson Education Canada Inc. Long-term Promissory Notes Term of note longer than one year. Can be bought and sold at any time before maturity. Subject to compound interest. No requirement to add the 3 days of grace in determining legal due date.

21. 9-20 Copyright © 2008 Pearson Education Canada Inc. Proceeds of Long-term Promissory Note

22. 9-21 Copyright © 2008 Pearson Education Canada Inc. Promissory Note Diagram Discount Period

23. 9-22 Copyright © 2008 Pearson Education Canada Inc. Calculating Proceeds of a Non- Interest-bearing Note

24. 9-23 Copyright © 2008 Pearson Education Canada Inc. Discounting an Interest- bearing Note Step 1 -- Find the maturity value of the note. Step 2 -- Find the present value at the discount date of the maturity value.

25. 9-24 Copyright © 2008 Pearson Education Canada Inc. Finding the Proceeds for an Interest-bearing Note

26. 9-25 Copyright © 2008 Pearson Education Canada Inc. Equivalent Values Equivalent values are the dated values of an original sum of money.

27. 9-26 Copyright © 2008 Pearson Education Canada Inc. Finding Equivalent Values Select a focal date. The focal date is a specific date chosen to compare the time values of one or more dated sums of money. If the due date of the payment falls before the focal date, use the FV formula. If the due date of the payment falls after the focal date, use the PV formula.

28. 9-27 Copyright © 2008 Pearson Education Canada Inc. Calculating Equivalent Values

29. 9-28 Copyright © 2008 Pearson Education Canada Inc. Summary With compound interest, earned interest is added to the principal and thus “interest is earned on interest” resulting in exponential growth. The future value of an investment at compound interest can be expressed by the formula FV = P(1+i) n. (continued)

30. 9-29 Copyright © 2008 Pearson Education Canada Inc. Summary (continued) The present value of a future amount at compound interest can be expressed by the formula PV = FV(1+i) -n.