2Section Objective Compute: the future value of an ordinary annuity the future value of an annuity due
3Key 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.
4Key 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.
5Formula 1Future Value = Amount of Deposit × Future Value of $1.00
6Formula 2 Future Value = Future Value of × ($1.00 + Rate of an Annuity Due Ordinary Annuity per Period)
7Understanding the Williams Sisters p. 217How often can you add deposits to your annuity account?
8Example 1Aiko 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?
9Example 1 Answer: Step 1 Find the total number of periods. Periods per Year × Number of Years4 × 2 = 8
10Example 1 Answer: Step 2 Find the interest rate per period. Annual Rate ÷ Number of Periods per Year6% ÷ 4 = 1.5%
11Example 1 Answer: Step 3Find 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
12Example 1 Answer: Step 4 Find the future value. Amount of Deposit × Future Value of $1.00$500 × = $4,216.42
13Example 2Suppose 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?
14Example 2 Answer: Step 1You know from Example 1 that the future value of the ordinary annuity is $4,
15Example 2 Answer: Step 2You also know that the rate per period is 1.5 percent or
16Example 2 Answer: Step 3Use the calculation for future value of an ordinary annuity due.Future Value of an Ordinary Annuity × ($ Rate per Period)$4, × ($ ) =$4, × = $4,279.67
17Practice 1Refer 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?
19Practice 2You 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?
20Practice 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