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SECTION 5-8 Annuities pp

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**Section Objective Compute: the future value of an ordinary annuity**

the future value of an annuity due

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**Key Words to Know annuity (p.217)**

An equal amount of money deposited into an account at equal periods of time. ordinary annuity (p. 217) An account in which equal deposits are made at the end of each interest period and start earning interest at the beginning of the next period.

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**Key Words to Know annuity due (p. 217)**

An account in which regular deposits are made at the beginning of each interest period and start earning interest immediately.

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Formula 1 Future Value = Amount of Deposit × Future Value of $1.00

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**Formula 2 Future Value = Future Value of × ($1.00 + Rate**

of an Annuity Due Ordinary Annuity per Period)

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**Understanding the Williams Sisters**

p. 217 How often can you add deposits to your annuity account?

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Example 1 Aiko Murakami deposits $500 in an ordinary annuity at the end of each quarter in an account earning 6 percent interest compounded quarterly. What is the future value of the account in 2 years?

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**Example 1 Answer: Step 1 Find the total number of periods.**

Periods per Year × Number of Years 4 × 2 = 8

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**Example 1 Answer: Step 2 Find the interest rate per period.**

Annual Rate ÷ Number of Periods per Year 6% ÷ 4 = 1.5%

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Example 1 Answer: Step 3 Find the future value of $1.00 for 8 periods at 1.5 percent per period using the Future Value of an Ordinary Annuity table on page 798 of your textbook. It is

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**Example 1 Answer: Step 4 Find the future value.**

Amount of Deposit × Future Value of $1.00 $500 × = $4,216.42

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Example 2 Suppose Aiko Murakami (from Example 1) had made $500 deposits in an annuity due at the beginning of each quarter in an account earning 6 percent interest compounded quarterly. What is the future value of the account in 2 years?

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Example 2 Answer: Step 1 You know from Example 1 that the future value of the ordinary annuity is $4,

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Example 2 Answer: Step 2 You also know that the rate per period is 1.5 percent or

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Example 2 Answer: Step 3 Use the calculation for future value of an ordinary annuity due. Future Value of an Ordinary Annuity × ($ Rate per Period) $4, × ($ ) = $4, × = $4,279.67

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Practice 1 Refer to the Future Value of an Ordinary Annuity for $1.00 per Period on page 798. Meredith Young deposits $1,500 in an ordinary annuity after each year for 8 years. The account pays 7 percent interest compounded annually. What is the future value of the account in 8 years?

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Practice 1 Answer $15,389.70

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Practice 2 You deposit $1,000 in an account each year at the beginning of the year. The account pays 8 percent interest compounded annually. What is the value of the account in 20 years? If you deposit $1,000 at the beginning of each year for 15 more years, what is the value of the account at the end of 35 years?

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**Practice 2 Answer Value of the account in 20 years: $49,422.92**

Value of the account at the end of 35 years: $186,102.14

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END OF SECTION 5-8 Overtime Pay

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