Financial Algebra© 2011 Cengage Learning. All Rights Reserved. Slide 1

3-7FUTURE 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

Financial Algebra© 2011 Cengage Learning. All Rights Reserved.

Warm-Up

Classify each exponential function as decreasing or increasing functions.

1. f(x) = 5x

2. f(x) = 0.5x

3. f(x) = (1.5)x

Slide 2

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

Financial Algebra© 2011 Cengage Learning. All Rights Reserved. Slide 4

Future value of a periodic deposit investment

1 1ntrP

nB r

n

B = balance at end of investment periodP = periodic deposit amountr = annual interest rate expressed as decimaln = number of times interest is compounded annuallyt = length of investment in years

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?

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

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

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?

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

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?

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

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.

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

Financial Algebra© 2011 Cengage Learning. All Rights Reserved.

Assignment

Pages 159 – 160, #2 – 8 even, 9

Slide 14