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

Planning Ahead

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

What are the advantages of having a savings account?

compound interest table

A tool to calculate compound interest quickly.

compound interest table

A tool to calculate compound interest quickly.

Lesson Objective Find compound interest using a table and the compound interest formula.

Content Vocabulary

compound interest table

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.)

Example 1Example 1

Find the total interest periods.

Periods per Year × Number of Years

4 quarters per year × 2 years = 8 periods

Example 1 Answer: Example 1 Answer: Step 1Step 1

Find the interest rate per period.

Periods per Year × Number of Years

Annual Rate ÷ Number of Periods per Year

6% ÷ 4 = 1.5%

Example 1 Answer: Example 1 Answer: Step 2Step 2

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.

Example 1 Answer: Example 1 Answer: Step 3Step 3

Find the amount.

Original Principal × Amount of $1.00

$3,000.00 × 1.12649 = $3,379.47

Example 1 Answer: Example 1 Answer: Step 4Step 4

Find the compound interest.

Amount – Original Principal

$3,379.47 – $3,000.00 = $379.47

Example 1 Answer: Example 1 Answer: Step 5Step 5

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?

Example 2Example 2

Find the total interest periods for first 6 months.

Periods per Year × Number of Years

4 quarters per year × ½ year = 2 periods

Example 2 Answer: Example 2 Answer: Step 1Step 1

Find the interest rate per period.

Annual Rate ÷ Number of Periods per Year

6% ÷ 4 = 1.5%

Example 2 Answer: Example 2 Answer: Step 2Step 2

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.

Example 2 Answer: Example 2 Answer: Step 3Step 3

Find the amount for 6 months.

Original Principal × Amount of $1.00

$4,379.47 × 1.03023 = $4,511.86 (new principal)

Example 2 Answer: Example 2 Answer: Step 4Step 4

Find the amount for 1.5 years.

Periods per Year × Number of Years

4 quarters per year × 1.5 years = 6 periods

Example 2 Answer: Example 2 Answer: Step 5Step 5

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.

Example 2 Answer: Example 2 Answer: Step 6Step 6

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

Example 2 Answer: Example 2 Answer: Step 7Step 7

$8,240 invested at 5.75 percent compounded semiannually for 3 years.

No additional deposits or withdrawals.

Find the amount.

Practice 1Practice 1

$8,240 x 1.18538 = $9,767.53

Practice 1 AnswerPractice 1 Answer

$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?

Practice 2Practice 2

$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 = 2,584.61 – 1900 = $684.61

Practice 2 AnswerPractice 2 Answer