1. Financial Algebra © 2011 Cengage Learning. All Rights Reserved. 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 © 2011 Cengage Learning. All Rights Reserved. Warm-UpWarm-Up Classify each exponential function as decreasing or increasing functions. 1.f(x) = 5 x 2.f(x) = 0.5 x 3.f(x) = (1.5) x Slide 2

3. Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Slide 3 future value of a single deposit investment – balance your account grows to at some point in the future periodic investment – same deposits made at regular intervals biweekly – every two weeks Key Terms

4. Financial Algebra © 2011 Cengage Learning. All Rights Reserved. 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 © 2011 Cengage Learning. All Rights Reserved. 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 © 2011 Cengage Learning. All Rights Reserved. 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 © 2011 Cengage Learning. All Rights Reserved. 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 © 2011 Cengage Learning. All Rights Reserved. Slide 8 Example 2 How much interest will Rich and Laura earn over the 20-year period?

9. Financial Algebra © 2011 Cengage Learning. All Rights Reserved. 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 © 2011 Cengage Learning. All Rights Reserved. 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 © 2011 Cengage Learning. All Rights Reserved. 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 © 2011 Cengage Learning. All Rights Reserved. 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 © 2011 Cengage Learning. All Rights Reserved. Slide 13 Construct a graph for Rich and Laura’s situation in Example 1. CHECK YOUR UNDERSTANDING

14. Financial Algebra © 2011 Cengage Learning. All Rights Reserved. AssignmentAssignment Pages 159 – 160, #2 – 8 even, 9 Slide 14