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**3-7 FUTURE VALUE OF INVESTMENTS**

Banking 4/6/2017 3-7 FUTURE VALUE OF INVESTMENTS OBJECTIVES Calculate the future value of a periodic deposit investment. Graph the future value function. Interpret the graph of the future value function. Chapter 1

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**Key Terms future value of a single deposit investment**

periodic investment biweekly future value of a periodic deposit investment

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**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

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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?

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**CHECK YOUR UNDERSTANDING**

How much more would Rich and Laura have in their account if they decide to hold off retirement for an extra year?

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

Example 2 How much interest will Rich and Laura earn over the 20-year period?

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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?

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**CHECK YOUR UNDERSTANDING**

Would opening an account at a higher interest rate for fewer years have assured Linda and Rob at least the same final balance?

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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.

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