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

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 Find compound interest using a table and the compound interest formula. Content Vocabulary • compound interest table compound interest table A tool to calculate compound interest quickly.

4. Example 1 State Bank pays 6 percent interest compounded quarterly on regular savings accounts. You deposited $3,000 for 2 years. You made no deposits or withdrawals. How much interest did you earn in 2 years? (Note: Use the Compound table on page A11 of your textbook to solve this problem.)

5. Example 1 Answer: Step 1 Find the total interest periods. Periods per Year × Number of Years 4 quarters per year × 2 years = 8 periods

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

7. Example 1 Answer: Step 3 Find the amount for 8 periods at 1.5 percent per period using the Compound Interest—Amount of $1.00 table on page A11 of your textbook. It is 1.12649.

8. Example 1 Answer: Step 4 Find the amount. Original Principal ×Amount of $1.00 $3,000.00 ×1.12649 = $3,379.47

9. Example 1 Answer: Step 5 Find the compound interest. Amount – Original Principal $3,379.47 – $3,000.00 = $379.47

10. Example 2 Juan Lopez opens an account and deposits $4,379.47. The account pays 6 percent annual interest and compounds quarterly. Six months later he deposits $2,000. How much will he have in the account in 1½ more years if he continues to pay 6 percent interest compounded quarterly?

11. Example 2 Answer: Step 1 Find the total interest periods for first 6 months. Periods per Year ×Number of Years 4 quarters per year × ½ year = 2 periods

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

13. Example 2 Answer: Step 3 Find the amount of $1.00 for 2 periods at 1.5 percent per period using the Compound Interest—Amount of $1.00 table on page 797. It is 1.03023.

14. Example 2 Answer: Step 4 Find the amount for 6 months. Original Principal ×Amount of $1.00 $4,379.47 ×1.03023 = $4,511.86 (new principal)

15. Example 2 Answer: Step 5 Find the amount for 1.5 years. Periods per Year ×Number of Years 4 quarters per year ×1.5 years = 6 periods

16. Example 2 Answer: Step 6 Find the amount of $1.00 for 6 periods at 1.5 percent per paid using the Compound Interest—Amount of $1.00 table on page 797. It is 1.09344.

17. Example 2 Answer: Step 7 Find the amount for 1.5 years. New Principal ×Amount of $1.00 ($4,511.86 + $2,000.00) ×1.09344 = $6,511.86 ×1.09344 = $7,120.33

18. Practice 1 $8,240 invested at 5.75 percent compounded semiannually for 3 years. No additional deposits or withdrawals. Find the amount.

19. Practice 1 Answer $8,240 x 1.18538 = $9,767.53

20. Practice 2 $1,900 invested at 6.25 percent compounded semiannually for 5 years. No additional deposits or withdrawals. Find the amount. How much interest did the money earn in 5 years?

21. Practice 2 Answer $1,900 invested at 6.25 percent compounded semiannually for 5 years: 1,900 x 1.36032 = $2,584.61 Interest earned in 5 years: 2,584.61 – 1900 = $684.61