annuities pp. 217-219 5-8 section. click to edit master text styles second level third level fourth...
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Annuities pp. 217-2195-8SECTIONSECTION
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Section ObjectiveSection ObjectiveCompute:
• the future value of an ordinary annuity
• the future value of an annuity due
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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.
Key Words to KnowKey Words to Know
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annuity due (p. 217)
An account in which regular deposits are made at the beginning of each interest period and start earning interest immediately.
Key Words to KnowKey Words to Know
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Future Value = Amount of Deposit × Future Value of $1.00
Formula 1Formula 1
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Future Value = Future Value of × ($1.00 + Rateof an Annuity Due Ordinary Annuity per Period)
Formula 2Formula 2
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Understanding the Williams Sisters Understanding the Williams Sisters p. 217p. 217
How often can you add deposits to your annuity account?
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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?
Example 1Example 1
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Find the total number of periods.
Periods per Year × Number of Years
4 × 2 = 8
Example 1 Answer: Example 1 Answer: Step 1Step 1
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Find the interest rate per period.
Annual Rate ÷ Number of Periods per Year
6% ÷ 4 = 1.5%
Example 1 Answer: Example 1 Answer: Step 2Step 2
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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 8.43284.
Example 1 Answer: Example 1 Answer: Step 3Step 3
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Find the future value.
Amount of Deposit × Future Value of $1.00
$500 × 8.43284 = $4,216.42
Example 1 Answer: Example 1 Answer: Step 4Step 4
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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?
Example 2Example 2
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You know from Example 1 that the future value of the ordinary annuity is $4,216.42.
Example 2 Answer: Example 2 Answer: Step 1Step 1
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You also know that the rate per period is 1.5 percent or 0.015.
Example 2 Answer: Example 2 Answer: Step 2Step 2
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Use the calculation for future value of an ordinary annuity due.
Future Value of an Ordinary Annuity × ($1.00 + Rate per Period)
$4,216.42 × ($1.00 + 0.015) =
$4,216.42 × 1.015 = $4,279.67
Example 2 Answer: Example 2 Answer: Step 3Step 3
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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?
Practice 1Practice 1
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$15,389.70
Practice 1 AnswerPractice 1 Answer
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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?
Practice 2Practice 2
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Value of the account in 20 years: $49,422.92
Value of the account at the end of 35 years: $186,102.14
Practice 2 AnswerPractice 2 Answer
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