Financial Algebra © Cengage Learning/South-Western 9/30/20149/30/2014 Warm-Up Sam deposits $4,000 into a CD that is continuously compounded. The CD pays 3.5% interest. How much money will Sam have after three years? Slide 1

Financial Algebra © Cengage/South-Western Slide 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

Financial Algebra © Cengage Learning/South-Western Slide 3 future value of a single deposit investment periodic investment biweekly future value of a periodic deposit investment Key Terms

Financial Algebra © Cengage Learning/South-Western Slide 4 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.

Financial Algebra © Cengage Learning/South-Western Future Value of Investment What are some different ways we have discussed people investing money so far this year? What are some different investment options we have discussed that are offered by banks? Do you think people only invest one large value of money at once, or do you think they continue to save money throughout their life as well? Slide 5

Financial Algebra © Cengage Learning/South-Western Future Value of Investment People are interested in what the balance of their investment will grow to in the future – the future value of their investment When people only invest money one time, they use the Compound interest formula B = P (1 + ) nt However, people usually continue to deposit money over and over again Slide 6

Financial Algebra © Cengage Learning/South-Western Future Value of Investment Periodic investments are the same deposits continuously made at regular intervals, such as yearly, monthly, biweekly, weekly, or even daily Many people get paid biweekly, or every other week, and deposit money into a savings account each pay check There are 26 biweekly paychecks in a year Slide 7

Financial Algebra © Cengage Learning/South-Western Slide 8 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

Financial Algebra © Cengage Learning/South-Western Slide 9 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 © 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?