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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

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future value of a single deposit investment periodic investment biweekly future value of a periodic deposit investment

Key Terms

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How can you effectively plan for the How can you effectively plan for the future balance in an account?future balance in an account?How can you effectively plan for the How can you effectively plan for the future balance in an account?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.

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Future value of a periodic deposit Future value of a periodic deposit investmentinvestmentFuture value of a periodic deposit Future value of a periodic deposit investmentinvestment

1 1nt

rP

nB

rn

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

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Example 1Example 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?

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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

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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

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Example 2Example 2

How much interest will Rich and Laura earn over the 20-year period?

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Use Example 1 Check Your Understanding. How much more interest would Rich and Laura earn by retiring after 21 years?

CHECK YOUR UNDERSTANDING

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EXAMPLE 3EXAMPLE 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?

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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

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EXAMPLE 4EXAMPLE 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.

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Construct a graph for Rich and Laura’s situation in Example 1.

CHECK YOUR UNDERSTANDING