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Planning Ahead Saving money is an important part of financial freedom and responsibility.

Planning Ahead Saving money is an important part of financial freedom and responsibility. What are the advantages of having a savings account?. Lesson Objective Compute the future value of an ordinary annuity and an annuity due. Content Vocabulary. annuity. annuity

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Planning Ahead Saving money is an important part of financial freedom and responsibility.

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  1. Planning Ahead Saving money is an important part of financial freedom and responsibility. What are the advantages of having a savings account?

  2. Lesson Objective Compute the future value of an ordinary annuity and an annuity due. Content Vocabulary • annuity annuity An account into which someone deposits an equal amount of money at equal periods or equal intervals of time. ordinary annuity An account in which equal deposits are made at eh end of each interest period. annuity due An account in which equal deposits are made at the beginning of the interest period and start earning interest immediately. • ordinary annuity • annuity due

  3. 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?

  4. Example 1 Answer: Step 1 Find the total number of periods. Periods per Year × Number of Years 4 × 2 = 8

  5. Example 1 Answer: Step 2 Find the interest rate per period. Annual Rate ÷ Number of Periods per Year 6% ÷ 4 = 1.5%

  6. 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 A12 of your textbook. It is 8.43284.

  7. Example 1 Answer: Step 4 Find the future value. Amount of Deposit × Future Value of $1.00 $500 ×8.43284 = $4,216.42

  8. 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?

  9. Example 2 Answer: Step 1 You know from Example 1 that the future value of the ordinary annuity is $4,216.42.

  10. Example 2 Answer: Step 2 You also know that the rate per period is 1.5 percent or 0.015.

  11. Example 2 Answer: Step 3 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

  12. Practice 1 Refer to the Future Value of an Ordinary Annuity for $1.00 per Period on page A12. 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?

  13. Practice 1 Answer 1500 x 10.25980 = $15,389.70

  14. 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?

  15. Practice 2 Answer Value of the account in 20 years: 1000 x 45.76196 x 1.08 = $49,422.92 Value of the account at the end of 35 years: 1000 x 172.31680 x 1.08 = $186,102.14

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