1. Financial Algebra © Cengage/South-Western Slide 1 3-7 FUTURE VALUE OF INVESTMENTS Calculate the future value of a periodic deposit investment. Graph the future value function. Interpret the graph of the future value function. OBJECTIVES

2. Financial Algebra © Cengage Learning/South-Western Slide 2 future value of a single deposit investment periodic investment biweekly future value of a periodic deposit investment Key Terms

3. Financial Algebra © Cengage Learning/South-Western Slide 3 How can you effectively plan for the future balance in an account? How can you calculate what the value of a deposit will be after a certain amount of time? If you want your balance to be a specific amount at the end of a period of time, how do you determine how much your initial deposit and subsequent deposits should be? Remember to consider the annual interest rate when considering your answer.

4. Financial Algebra © Cengage Learning/South-Western Slide 4 Future value of a periodic deposit investment B = balance at end of investment period P = periodic deposit amount r = annual interest rate expressed as decimal n = number of times interest is compounded annually t = length of investment in years

5. Financial Algebra © Cengage Learning/South-Western Slide 5 Example 1 Rich and Laura are both 45 years old. They open an account at the Rhinebeck Savings Bank with the hope that it will gain enough interest by their retirement at the age of 65. They deposit $5,000 each year into an account that pays 4.5% interest, compounded annually. What is the account balance when Rich and Laura retire?

6. Financial Algebra © Cengage Learning/South-Western Slide 6 How much more would Rich and Laura have in their account if they decide to hold off retirement for an extra year? CHECK YOUR UNDERSTANDING

7. Financial Algebra © Cengage Learning/South-Western Slide 7 Carefully examine the solution to Example 1. During the computation of the numerator, is the 1 being subtracted from the 20? Explain your reasoning. EXTEND YOUR UNDERSTANDING

8. Financial Algebra © Cengage Learning/South-Western Slide 8 Example 2 How much interest will Rich and Laura earn over the 20-year period?

9. Financial Algebra © Cengage Learning/South-Western Slide 9 Use Example 1 Check Your Understanding. How much more interest would Rich and Laura earn by retiring after 21 years? CHECK YOUR UNDERSTANDING

10. Financial Algebra © Cengage Learning/South-Western Slide 10 EXAMPLE 3 Linda and Rob open an online savings account that has a 3.6% annual interest rate, compounded monthly. If they deposit $1,200 every month, how much will be in the account after 10 years?

11. Financial Algebra © Cengage Learning/South-Western Slide 11 Would opening an account at a higher interest rate for fewer years have assured Linda and Rob at least the same final balance? CHECK YOUR UNDERSTANDING

12. Financial Algebra © Cengage Learning/South-Western Slide 12 EXAMPLE 4 Construct a graph of the future value function that represents Linda and Rob’s account for each month. Use the graph to approximate the balance after 5 years.

13. Financial Algebra © Cengage Learning/South-Western Slide 13 Construct a graph for Rich and Laura’s situation in Example 1. CHECK YOUR UNDERSTANDING