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UNIT 7

© Houghton Mifflin Harcourt Publishing Company • Image Credits: ©aberCPC/Alamy

Personal Financial Literacy

MODULE MODULE

13 13

Taxes, Interest, and Incentives 7.13.A, 7.13.E, 7.13.F

14 14 Planning Your Future

MODULE MODULE

7.13.B, 7.13.C, 7.13.D

CAREERS IN MATH Freelance Computer Programmer A computer programmer translates commands into code, a language that a computer understands. Programmers work on a variety of tasks, from creating computer games to testing software. A freelance programmer doesn’t work for a specific company; this gives the freelancer more flexibility with his or her work schedule. Computer programmers use mathematical logic when writing or altering code. If you are interested in a career as a computer programmer, you should study these mathematical subjects: • Algebra • Geometry • Trigonometry • Calculus • Discrete Math Research other careers that require the understanding of mathematical logic.

Unit 7 Performance Task At the end of the unit, check out how a freelance computer programmer uses math. Unit 7

399

UNIT 7

Vocabulary

Preview

Use the puzzle to preview key vocabulary from this unit. Unscramble the circled letters within found words to answer the riddle at the bottom of the page.

S M F S A O I N P H C M F C E

400

T Y S K F R V G E Q K I G M Y

E J R K B Z N P Z T X P O G F

S I N S P R P G M E W C K J M

S R D P E P B M D L N O P Q C

A Z N S M A G E D I T K R U T

Y K M O K U X N C A U Y J T L

N W R D C P N R E B L G W P H

F I J A E V E J C I J K W P Y

N Q A N B N C A A L G T K W E

M C S W W K Z K U I C U R U H

B E V J H H W Z K T B C Y N S

S H F I Q Q O X L I Y U R A M

K Y C Z E B U D G E T C D B U

The things you own that have a positive cash value. (Lesson 14.3)



The amount of money you earn. (Lesson 14.1)



A plan for managing your money to help you reach your financial goals. (Lesson 14.1)



Debts you owe that have a negative cash value. (Lesson 14.3)



Expenses that occur regularly and stay the same (2 words). (Lesson 14.1)



The difference between assets and liabilities (2 words). (Lesson 14.3)

Vocabulary Preview

© Houghton Mifflin Harcourt Publishing Company



U F A R M O R P X S K L L Z C

Q:

What did the fisherman give to the IRS?

A:

His

!

Taxes, Interest, and Incentives ?

MODULE

13

LESSON 13.1

ESSENTIAL QUESTION

Calculating Sales and Income Tax

How can you solve realworld problems involving taxes, interest, and incentives?

7.13.A

LESSON 13.2

Calculating and Comparing Simple and Compound Interest 7.13.E

LESSON 13.3

Making Purchasing Decisions

© Houghton Mifflin Harcourt Publishing Company • Image Credits: ©NAN/Alamy Images

7.13.F

Real-World Video

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You can invest money in savings accounts, certificates of deposit (CDs), and bonds. Each type of investment earns simple or compound interest, so your money grows over time.

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Math On the Spot

Animated Math

Personal Math Trainer

Go digital with your write-in student edition, accessible on any device.

Scan with your smart phone to jump directly to the online edition, video tutor, and more.

Interactively explore key concepts to see how math works.

Get immediate feedback and help as you work through practice sets.

401

Are YOU Ready? Personal Math Trainer

Complete these exercises to review skills you will need for this chapter.

Percents and Decimals EXAMPLE

125% = 100% + 25%

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Online Assessment and Intervention

100 ___ 25 + 100 = ___ 100

Write the percent as the sum of 1 whole and a percent remainder. Write the percents as fractions.

= 1 + 0.25

Write the fractions as decimals.

= 1.25

Simplify.

Write each percent as a decimal. 1. 45%

2. 91%

3. 8%

4. 111%

7. 0.05

8. 1.98

Write each decimal as a percent. 5. 0.79

6. 0.8

Decimal Operations EXAMPLE

25.9 − 3.24 → 25.90 − 3.24 22.66

To add or subtract decimals, align the decimal points. Add zeros if necessary.

9. 11.9 − 7.6

10. 24.1 − 9.25

11. 45 − 10.6

12. 6.04 − 3.5

13. 5.17 − 5.09

14. 100 − 3.77

Multiply with Fractions and Decimals EXAMPLE

5.9 × 3.6 354 +177 2 1.2 4

Multiply as you would with whole numbers. Count the total number of decimal places in the two factors. Write the same total number of decimal places in the product.

Multiply. 15.

402

Unit 7

2.77 × 24

16.

9.95 × 0.7

17. 12.04 × 3.2

18.

38.4 × 0.72

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Find each sum or difference.

Reading Start-Up

Vocabulary Review Words

Visualize Vocabulary

deductions (deducciones) ✔ federal withholding (retención fiscal federal) gross pay (paga bruta) ✔ income tax (impuesto sobre la renta) net pay (paga neta) principal (capital) ✔ sales tax (impuesto sobre la venta) ✔ taxable income (ingreso sujeto a impuestos) unit price (precio por unidad)

Use the ✔ words to complete the graphic. You will put a different word in each box. Money employers deduct from wages:

Taxes due on April 15 of each year:

Understanding Taxes

Percent of the total cost of goods sold:

Income that is taxed:

Preview Words compound interest (interés compuesto) interest (interés) simple interest (interés simple)

Understand Vocabulary Complete each sentence using the preview words.

1. The amount of money earned by bank customers based on the

© Houghton Mifflin Harcourt Publishing Company

amount of principal in their savings account is

2.

.

is interest paid only on the principal, according to an agreed upon interest rate.

Active Reading Tri-Fold Before beginning the module, create a tri-fold to help you learn the concepts and vocabulary in this module. Fold the paper into three sections. Label the columns “What I Know,” “What I Need to Know,” and “What I Learned.” Complete the first two columns before you read. After studying the module, complete the third column.

Module 13

403

MODULE 13

Unpacking the TEKS Understanding the TEKS and the vocabulary terms in the TEKS will help you know exactly what you are expected to learn in this module.

7.13 Develop an economic way of thinking and problem solving useful in one’s life as a knowledgeable consumer and investor.

Key Vocabulary taxable income (ingreso sujeto a impuestos) The total amount of income minus deductions. sales tax (impuesto sobre la venta) A percent of the total cost of goods and services.

What It Means to You You will learn how each of the following standards related to 7.13 is designed to help you understand your taxes, interest and incentives. 7.13.A Calculate the sales tax for a given purchase and calculate income tax for earned wages. 7.13.E Calculate and compare simple interest and compound interest earnings. 7.13.F Analyze and compare monetary incentives, including sales, rebates, and coupons.

principal (capital) The money you put in a savings account. interest (interés) Money paid to you by the bank to allow them to borrow your money.

compound interest (interés compuesto) Interest paid on the principal and on the interest an account has earned.

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404

Unit 7

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simple interest (interés simple) Interest paid only on the original principal.

LESSON

13.1 ?

Calculating Sales and Income Tax

Personal financial literacy— 7.13.A Calculate the sales tax for a given purchase and calculate income tax for earned wages.

ESSENTIAL QUESTION How do you calculate sales tax and income tax?

Calculating Sales Tax Sales tax is a tax imposed by state or local governments. It is collected by the seller or service provider. The tax is a percent of the total cost of goods and services. Sales tax rates vary by region and not all items are taxable.

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EXAMPL 1 EXAMPLE

7.13.A

Rafiq purchases products from a nursery for his yard. The table shows his purchases and the prices. The sales tax rate is 7.5%. Find the total cost of his purchase, including tax. STEP 1

Find the tax on each item.

Math Talk

Mathematical Processes

Black-Eyed Susan: ($6.25 · 2) · 7.5%

What is another way to find the total cost?

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$12.50 · 0.075 = 0.9375 = 0.94 STEP 2

Add the subtotal and the tax on each item to find its total price. Add to find the total cost of his purchase. $12.50 + 0.94 = $13.44 Item

Unit price Number Subtotal Tax (7.5%)

Total

Black-Eyed Susan

$6.25

2

$12.50

$0.94

$13.44

Coneflower

$6.99

5

$34.95

$2.62

$37.57

Mexican White Oak

$29.99

1

$29.99

$2.25

$32.24

Total cost

$83.25

The total cost of his purchase is $83.25.

Multiply the subtotal for each product by the tax rate of 7.5%, or 0.075.

YOUR TURN 1. What If? Suppose Rafiq returned to the nursery and bought a second tree priced at $49.99 and two packages of fertilizer priced at $12.99 each. Find the total cost of his purchase, including tax.

Personal Math Trainer Online Assessment and Intervention

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Lesson 13.1

405

Calculating Withholding Most workers pay yearly federal income taxes based on the wages, or pay, they earn. Employers deduct money called federal withholding from workers’ wages, and send it to the federal government as partial payment of the workers’ yearly income tax. Each year around April 15, workers submit a federal income tax return. At that time, they may owe additional taxes or may get a refund depending on several factors, including the amount already paid through withholding.

Math On the Spot my.hrw.com

A worker’s pay before any amounts are deducted, or taken out, is called gross pay. Net pay is gross pay less all deductions, including withholding. net pay

=

gross pay



total deductions

EXAMPLE 2

7.13.A

Quinn’s gross monthly pay is $2,050. Federal withholding is 11.4% of her gross pay. Part of her monthly pay statement is shown in Step 2 below. Find Quinn’s net pay after all deductions. Find the amount that is deducted for federal withholding. Federal withholding = $2,050 × 0.114 = $233.70 STEP 2

Find the total deductions. GROSS PAY Monthly Wages

Math Talk

Mathematical Processes

Tomas pays 6.2% of his gross monthly pay, or $316.20 for Social Security. What is his gross monthly pay? Explain.

TAXES Federal Withholding Social Security (6.2%) Medicare (1.45%)

Social Security (or FICA) and Medicare are federally mandated deductions and are calculated as percents of gross income.

$2,050.00 $233.70 $127.10 $29.73

Total deductions = $233.70 + $127.10 + $29.73 = $390.53 net pay = gross pay - total deductions = $2,050.00 - $390.53 = $1,659.47 Quinn’s net pay each month is $1,659.47.

YOUR TURN 2. Personal Math Trainer Online Assessment and Intervention

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406

Unit 7

Arnetta’s monthly gross pay is $4,200. Federal withholding is 16.05% of her pay. Her other deductions total $321.30. Find her net pay.

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STEP 1

Calculating Income Tax Federal income taxes are based on an individual’s taxable income. Taxable income is the total amount of income minus deductions. taxable income

=

gross income



Math On the Spot

total deductions

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Taxpayers may take a standard deduction set by the Internal Revenue Service (IRS), or they may itemize deductions such as property taxes or medical expenses. Income tax is the product of the tax rate and the taxable income. Many taxpayers use a tax table provided by the IRS.

EXAMPL 3 EXAMPLE

Problem Solving

7.13.A

After deductions, Jonah has a taxable income of $26,318. He paid a total of $4,059 in federal withholding. Find the tax due on Jonah’s income. Then tell whether he will have to pay an additional amount or will get a refund. Analyze Information

Identify the important information. • Jonah’s taxable income is $26,318. • Jonah already paid $4,059 in federal withholding. Formulate a Plan

Use a tax table to find the amount of tax owed on $26,318. Then compare the tax due with the tax withheld. Solve STEP 1

Use a tax table to find the tax for a gross income of $26,318.

© Houghton Mifflin Harcourt Publishing Company

If line 43 (taxable income is —

STEP 2

And you are single

At least

But less than

Your tax is —

26,200

26,250

3,509

26,250

26,300

3,516

26,300

26,350

3,524

26,350

26,400

3,531

$26,318 is between 26,300 and 26,350.

Compare the tax due of $3,524 with the tax withheld of $4,059. $4,059 - $3,524 = $535 Jonah paid $535 more than he owes.

Justify and Evaluate

Jonah paid $4,059. His tax from the tax table was $3,524, which is a lesser number. This means Jonah paid more in taxes than he owes. He will get $535 back as a refund. Lesson 13.1

407

YOUR TURN Personal Math Trainer

3.

Online Assessment and Intervention

Glenda’s taxable income is $26,222. She paid $2,640 in federal withholding. Find the tax due on Glenda’s income. Then tell whether she will have to pay an additional amount or will get a refund. Use the tax table in Example 3.

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Guided Practice Find each amount. Use a sales tax rate of 8%. (Example 1) Product description

Unit price

Number

Subtotal

1.

Pens (3 pack)

$3.59

3

$10.77

2.

Notebooks (2 pack)

$1.99

2

$3.98

3.

Backpack

$44.99

1

$44.99

4.

Highlighters (4 pack)

$5.15

1

$5.15

5.

Tax (8%)

Total

Total cost

7. Lizaveta’s taxable income is $26,380. She paid $2,940 in federal withholding. Use a problem solving model to determine whether she will have to pay an additional amount or will get a refund. Use the tax table in Example 3. (Example 3)

? ?

ESSENTIAL QUESTION CHECK-IN

8. Suppose the sales tax rate in your area is 7.5%. Explain how to determine the total cost, including tax, of an eReader that costs $125.

408

Unit 7

© Houghton Mifflin Harcourt Publishing Company

6. Juan earns a monthly salary of $3,200. Federal withholding is 14.1% of his gross pay. Juan has a total of $244.80 deducted for Social Security and Medicare. Find his net pay. (Example 2)

Name

Class

Date

13.1 Independent Practice 7.13.A

Personal Math Trainer my.hrw.com

Online Assessment and Intervention

9. Roland is purchasing pottery supplies for his pottery class. He buys a portable pottery wheel for $382.00, modeling clay for $12.00, and a pottery tool set for $16.14. If the tax rate is 8.25%, find the total tax he paid. Then find the total cost of his purchases.

10. Megna has $300 to buy a digital camera. She finds one she likes that costs $275. a. Suppose the tax rate is 7.3%. Does Megna have enough to buy the camera? Explain.

b. Megna discovers that the digital camera needs a memory card. She finds a memory card on sale for $9.99 plus tax. Can Megna afford the card?

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11. Casey is looking at the used car shown. Suppose that Casey is able to get $1,200 in trade for his old vehicle. The sales tax rate is 7.75%. How much will Casey pay in taxes on the reduced sales price?

12. What’s the Error? Lauren wants to buy 3 shirts at $15.00 each. At home, she calculates the total cost as $46.20, using the sales tax rate of 8%. At the store, the cashier tells Lauren the total cost is $48.60. Who is wrong and what mistake did he or she make?

13. Camden earns $25 per hour, and works 40 hours a week. a. Camden gets paid every 2 weeks. Federal withholding is 15.6% of his gross pay, Social Security is 6.2% of his gross pay, and Medicare is 1.45%. Find Camden’s net pay after 2 weeks. Show your work.

b. What If Suppose Camden gets a raise of $5 per hour and pays 17.2% of his gross pay in federal withholding. What would his net pay for 2 weeks be? Make sure to factor in his social security and Medicare withholdings.

Lesson 13.1

409

14. Critique Reasoning Samantha said adding 6% to the cost of an item for sales tax makes the total cost 106% of the original price. Joshua disagrees. Is Samantha’s reasoning accurate? Explain.

15. After deductions, Elizabeth’s taxable income was $28,536. She had $344 withheld each month for taxes. Use the tax table shown to find how much she will get as a refund or owe. If line 43 (taxable income is −

And you are single

At least

But less than

Your tax is −

28,400

28,450

3,839

28,450

28,500

3,846

28,500

28,550

3,854

28,550

28,600

3,861

FOCUS ON HIGHER ORDER THINKING

Work Area

17. Multistep Suppose the personal income tax rate is changed to a flat rate of 15% of one’s taxable income. Use the tax table in problem 15 to investigate the effect of the change in the rate on a single taxpayer with a taxable income of $28,443.

18. Represent Real-World Problems You have $3,000 to spend on a laptop. Suppose the tax rate is 6.78%. What is the maximum you can spend on a laptop if you know you will also be purchasing a $25 case? Explain.

410

Unit 7

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16. Persevere in Problem Solving A family buys groceries for $149.98, including $10.07 in taxes. The bill includes $26.95 worth of items that are not taxable. Find the sales tax rate. Round your answer to the nearest tenth of a percent.

Calculating and Comparing Simple and Compound Interest

LESSON

13.2 ?

Personal financial literacy— 7.13.E Calculate and compare simple interest and compound interest earnings.

ESSENTIAL QUESTION How do you calculate simple and compound interest?

Calculating Simple Interest Recall that the money you put in a savings account is called principal. The bank pays you interest at an agreed upon interest rate. Simple interest is interest paid only on the principal, and is paid out to the person who owns the account. It is not kept on deposit to earn more interest.

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EXAMPL 1 EXAMPLE

7.13.E

Roberto’s parents open a savings account for him on his birthday. The account earns simple interest at an annual rate of 5%. They deposit $100 and will deposit $100 on each birthday after that. Roberto will make no withdrawals from the account for at least 10 years. Make a table to show how the interest accumulates over five years.

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Deposit Beginning balance Amount New Interest Amount of phase for new phase $ deposited $ balance $ rate % interest earned $ 1

0

100

100

5

5

2

100

100

200

5

10

3

200

100

300

5

15

4

300

100

400

5

20

5

400

100

500

5

25

Total

75

Roberto earns a total of $75 in interest over the five years.

Reflect 1.

Make a Prediction Predict how much simple interest Roberto will have earned after the tenth year. Suppose he continues to make no withdrawals.

YOUR TURN 2.

Each year Amy deposits $100 into an account that earns simple interest at an annual rate of 8%. How much interest will she earn over the first five years? How much will be in her account after that time?

Personal Math Trainer Online Assessment and Intervention

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Lesson 13.2

411

Calculating Compound Interest Most banks pay compound interest. That is, interest earned is kept on deposit to earn more interest. Compound interest is computed on the entire amount in the account, including the principal, and any previously interest earned.

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EXAMPLE 2

7.13.E

On Claudia’s birthday, her parents open a savings account and deposit $100. They also deposit $100 each year after that on her birthday. The account earns interest at an annual rate of 5% compounded annually. Claudia will make no withdrawals from the account for at least 10 years. Make a table to find the ending balance in Claudia's account after 5 years. Beginning Deposit balance Amount New Interest for deposited phase new phase $ balance $ rate % $

Amount of interest earned $

Ending balance $

Math Talk

1

0.00

100

100.00

5

5.00

105.00

Mathematical Processes

2

105.00

100

205.00

5

10.25

215.25

How can you find the total amount of interest that accumulates over the five years?

3

215.25

100

315.25

5

15.76

331.01

4

331.01

100

431.01

5

21.55

452.56

5

452.56

100

552.56

5

27.63

580.19

The total amount in the account at the end of the fifth year is $580.19.

3.

Does the balance of Claudia’s account change by the same amount each year? Explain why or why not.

4.

Would the total amount in the account after 5 years be greater if the interest rate were higher? Explain.

YOUR TURN Personal Math Trainer Online Assessment and Intervention

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412

Unit 7

5.

What If? Suppose the interest rate on Claudia’s account is 6% instead of 5%. How much will Claudia have in her account at the end of the fifth year? How does it compare to the amount in Example 2?

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Reflect

Comparing Simple and Compound Interest You can use a formula for compound interest compounded annually to solve problems.

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Compound Interest Compounded Annually A = P(1 + r)t, where P is the principal (the original amount deposited), r is the interest rate expressed as a decimal, t is the time in years, and A is the amount in the account after t years if no withdrawals are made.

EXAMPL 3 EXAMPLE

7.13.E

Jane has two savings accounts, Account S and Account C. Both accounts are opened with an initial deposit of $100 and an annual interest rate of 5%. No additional deposits are made, and no withdrawals are made. Account S earns simple interest, and Account C earns interest compounded annually. Which account will earn more interest after 10 years? How much more? STEP 1

Find the total interest earned by Account S after 10 years. Find the amount of interest earned in one year. Principal $100

× Interest rate

= Interest for 1 year

×

=

0.05

$5

Find the amount of interest earned in ten years.

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Interest for 1 year × Number of years = Interest for 10 years $5

×

=

10

$50

Account S will earn $50 after 10 years. STEP 2

Find the final amount in Account C. Then subtract the principal to find the amount of interest earned.

(1 + 0.05)10 means you have 10 factors of 1.05.

A = P(1 + r)t

Use the compound interest formula.

= 100 × (1 + 0.05)10 Substitute 100 for P, 0.05 for r, 10 for t. = 162.89

Calculate. Round to the nearest cent.

Account C will earn $162.89 - $100.00 = $62.89 after 10 years. STEP 3

Compare the amounts using subtraction: $62.89 - $50 = $12.89 Account C earns $12.89 more in compound interest after 10 years than Account S earns in simple interest.

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Lesson 13.2

413

YOUR TURN Personal Math Trainer

6.

Online Assessment and Intervention

What If? Suppose the accounts in Example 3 both have interest rates of 4.5%. Which account will earn more interest after 10 years? How much more?

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Guided Practice 1. Each year on the same day, Hasan deposits $150 in a savings account that earns simple interest at an annual rate of 3%. He makes no other deposits or withdrawals. How much interest does his account earn after one year? After two years? After five years? (Example 1)

Keri deposits $100 in an account every year on the same day. She makes no other deposits or withdrawals. The account earns an annual rate of 4% compounded annually. Complete the table. (Example 2) Deposit Beginning balance Amount New Interest phase for new phase $ deposited $ balance $ rate %

2.

1

0.00

100

3.

2

104.00

100

4

4.

3

100

4

5.

4

100

4

6.

5

100

4

4

7. Theo deposits $2,000 deposit in a savings account earning compound interest at an annual rate of 5% compounded annually. He makes no additional deposits or withdrawals. Use the formula for compound interest to find the amount in the account after 10 years. (Example 3)

? ?

ESSENTIAL QUESTION CHECK-IN

8. Describe the difference between simple interest and compound interest.

414

Unit 7

© Houghton Mifflin Harcourt Publishing Company

100.00

Amount of interest Ending balance $ earned $

Name

Class

Date

13.2 Independent Practice

Personal Math Trainer

7.13.E

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Online Assessment and Intervention

Mia borrowed $5,000 from her grandparents to pay college expenses. She pays them $125 each month, and simple interest at an annual rate of 5% on the remaining balance of the loan at the end of each year. 9. How many months will it take her to pay the loan off? Explain.

10. For how many years will she pay interest? Explain.

11. How much simple interest will she pay her grandparents altogether? Explain.

© Houghton Mifflin Harcourt Publishing Company

12. Roman saves $500 each year in an account earning interest at an annual rate of 4% compounded annually. How much interest will the account earn at the end of each of the first 3 years?

13. Jackson started a savings account with $25. He plans to deposit $25 each month for the next 12 months, then continue those monthly deposits in following years. The account earns interest at an annual rate of 4% compounded annually, based on his final yearly balance. Fill in the chart to find out how much money he will have in the account after 3 years. Deposit Beginning balance phase for new phase $ 1

25.00

Amount deposited New Interest by year end $ balance $ rate % 300.00

325.00

Amount of interest earned $

Ending balance $

4

2 3

Lesson 13.2

415

14. Communicate Mathematical Ideas Look back at Exercise 13. Suppose Jackson increased the initial deposit by $75, but made the same monthly deposits. Would the balance at the end of every year increase by $75?

15. Account A and Account B both have a principal of $1,000 and an annual interest rate of 4%. No additional deposits or withdrawals are made. Account A earns simple interest. Account B earns interest compounded annually. Compare the amounts in the two accounts after 20 years. Which earns more interest? How much more?

FOCUS ON HIGHER ORDER THINKING

Work Area

16. Justify Reasoning Luisa deposited $2,000 in an account earning simple interest at an annual rate of 5%. She made no additional deposits and no withdrawals. When she closed the account, she had earned a total of $2,000 in interest. How long was the account open?

18. Persevere in Problem Solving Gary invested $1,000 in an account earning interest at an annual rate of 5% compounded annually. Each year, he deposited an additional $1,000, and made no withdrawals. When he closed the account, he had a balance of $4,525.64. Make a table similar to the one in Example 2 to help you estimate how long the money was in the account. How much interest would Gary earn in that same time if he invests $10,000 and deposits $10,000 into the account each year?

416

Unit 7

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17. Draw Conclusions Amanda deposits $500 into a savings account earning simple interest at an annual rate of 8%. Tori deposits $1,000 into a savings account earning simple interest at an annual rate of 2.5%. Neither girl makes any additional deposits or withdrawals. Which girl’s account will reach a balance of $1,500 first? Justify your answer.

Making Purchasing Decisions

LESSON

13.3 ?

ESSENTIAL QUESTION

Personal financial literacy—7.13.F Analyze and compare monetary incentives, including sales, rebates, and coupons.

How do you decide on the best purchase among various options?

Using Unit Prices You often need to make purchasing decisions based upon price. Finding the lower unit price is often the way to determine the better buy.

EXAMPL 1 EXAMPLE

7.13.F

Math On the Spot my.hrw.com

Silvie went to a local warehouse store to buy her family’s favorite sports drink. Which of the two options described below is the better buy?

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STEP 1

Value Pack

Sport Pack

24 0.5-liter bottles

18 0.75-liter bottles

$9.24

$11.88

Find the total amount of the sports drink in each purchase. Value Pack: 24(0.5) = 12 liters Sport Pack: 18(0.75) = 13.5 liters

STEP 2

Multiply the number of bottles by the number of ounces.

Find each unit price. Value Pack $9.24 ______ = $0.77 per liter 12 liters

Sports Pack $11.88 _______ = $0.88 per liter 13.5 liters

The Value Pack is a better buy, because $0.77 < $0.88.

Math Talk

Mathematical Processes

Suppose a very large box of cereal has a lower unit price than a small box. Why might the small box be the better choice for you?

YOUR TURN 1. Financial Literacy Manny must choose between a pack of four 6.5-ounce containers of yogurt for $3.77 or three 8-ounce containers at $1.29 each. Which is the better buy? Why? Personal Math Trainer Online Assessment and Intervention

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Lesson 13.3

417

Analyzing Sales Math On the Spot my.hrw.com

Sales and discounts may affect your choice when considering several purchase options. Some discounts are fixed amounts, while others are percents or fractions of the original price.

EXAMPLE 2

7.13.F

Nathan plans on hiking this summer and wants to buy a solar charger for his cell phone and notebook computer. He finds the charger that he wants at two stores. Which store has the lower price for the charger? Regular price

Discount

Kitt’s

$89.99

30% off

Rec Plus

$79.99

$15 off

STEP 1

Find the discount price at each store. Kitt’s

Rec Plus

To the nearest cent, the discount price at Kitt’s is $62.99. STEP 2

The discount price at Rec Plus is $64.99.

Compare the discounted prices. Kitt’s offers the lower price, because $62.99 < $64.99.

Reflect 2. Critical Thinking Why might Nathan choose the higher priced item?

YOUR TURN Personal Math Trainer Online Assessment and Intervention

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Unit 7

3. Nathan finds a backpack at Kitt’s that is regularly $84.99, but is on sale for _1 off. The same backpack is regularly $72.99 at Rec Plus but is on sale for 3 25% off. Which is a better buy? Explain.

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discount regular - discount discount regular - discount = = price price price price = $89.99 - 0.3($89.99) = $79.99 - $15.00 = $89.99 - $26.997 = $64.99 = $62.993

Comparing Sales, Rebates, and Coupons When you buy an item on sale or use a discount coupon, you pay less than full price for the item and generally pay tax on the sale price. When you get a rebate, you usually pay full price for the item and the tax on that price, and then get a refund later.

EXAMPL 3 EXAMPLE

7.13.F

Cedelia can get the same running shoes at two different stores. She wants to get two pairs of the same style. Which is the better buy?

Go Run Regular price: $109 $5 off:

-5

Total:

$104

She pays $104 for 2 pairs.

Go Run

Shoe Shoppe

Reg. price: $109

Reg. price: $89

Take $5 off 1 pair.

Mail-in rebate: $30 per pair (limit 2)

Buy 1 pair, get 1 pair free.

Math On the Spot my.hrw.com

My Notes

Shoe Shoppe Regular price: $89 Rebate: Total:

- 30 $59

She pays 2 × $59 = $118 for 2 pairs.

Go Run has the better buy because $104 < $118.

Reflect

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4. What If? Suppose the total price at Shoe Shoppe had been $103? What are some conditions of a rebate that would make it a better decision to buy the shoes at Go Run?

YOUR TURN 5. Greta wants to buy 3 jars of honey. Food Mart sells it for $8.99 with a “Buy 2, get 1 free” offer. Leona’s sells it for $8.49 with a coupon for 50% off with a limit of 2 coupons. Which store has the better deal?

Personal Math Trainer Online Assessment and Intervention

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Lesson 13.3

419

Guided Practice Which is the better buy? Write an inequality to justify your answer. 1. The Corner Store sells 4 bottles of energy drink for $11.56. Bev’s sells 6 bottles for $17.94. Which is the better buy? (Example 1) _________ =

/bottle

_________ =

/bottle

2. You can buy a 2-pound loaf of bread for $2.50 or a 2-pack of 1_12 -pound loaves for $3.30. Which is the better buy? (Example 1)

3. Marta can buy a 6-pack of 15-ounce cans of broth for $11.29 or three 32-ounce containers for $10.97. Which is the better buy? (Example 1)

$11.29 _______ ≈ 

oz  /oz

3(32)

oz

$10.97 _______ ≈ 

 /oz

4. Zena can get an item online for $19 that weighs 8 pounds. Shipping and handling costs $0.49 per pound. She can also buy the same item locally for $26.95, and she has a $5 off coupon. Which is the better buy? (Example 2)

5. A take-and-bake pizza chain has several coupons, which cannot be used together. J.D. is buying a pizza that costs $17.90. Should he use a $5 off coupon or a 35% off coupon? (Example 2)

6. The King family buys an HDTV selling for $825 at PanView with a 20% off coupon and a rebate of $125. They later see the TV on sale at Rey’s TVs for $555. Did they get the better deal? (Example 3)

7. Credit card A has an annual fee of $50 but gives you a rebate at the end of the year of 2% of your total purchases. Credit card B has no annual fee or rebate. If you spend about $150 a month, which card is better for you? (Example 3)

? ?

ESSENTIAL QUESTION CHECK-IN

8. Is the lower unit price always the best buy?

420

Unit 7

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6(15) =

Name

Class

Date

13.3 Independent Practice 7.13.F

Personal Math Trainer my.hrw.com

Online Assessment and Intervention

9. Store 1 has a price of $99 on an MP3 player. Store 2 is offering the same MP3 player at a sale price of 25% off their regular price of $125. Jerusha wants to buy an MP3 player. From which store should she buy it? Explain.

10. Multistep Randy wants trail mix for his hiking trip. The ready-made trail mix costs $8.95 for 1.5 pounds. The costs of the bulk ingredients to make one pound of trail mix are as follows: salted peanuts—$1.25, raisins—$1.70, sunflower seeds—$0.50, cashews—$0.87, and almonds—$0.65. If Randy plans to take 6 pounds of trail mix, which option is cheaper? How much does he save by choosing the cheaper option?

11. Tyron and Penelope both bought 4-wheelers. Tyron paid $199 up front, and will pay the remainder in 12 payments of $50 each. Penelope paid nothing up front, and will make 18 payments of $49. Who got the better buy? Explain.

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12. Financial Literacy T’Shonda is buying a laptop computer. She will pay 8% sales tax on the price before any rebates. Where will she get a better buy? Explain.

13. Critical Thinking What single discount is equal to a 1 discount of _4 off followed by an additional 10% off the sale price?

14. Make a Conjecture John is comparing the prices of two bags of the same cereal. He notices that the larger bag holds 10 more ounces and costs $1.50 more. How can he use the unit price of the smaller bag to decide the better buy? Explain.

Lesson 13.3

421

FOCUS ON HIGHER ORDER THINKING

Work Area

15. Draw Conclusions Mr. Jaros has the following options for buying a digital video recorder and access to the recording service for 2 years. DiV: $49.99 digital video recorder, 2-year subscription at $16.98 a month TVU: Free digital video recorder, 2-year commitment at $19.95 a month a. Which is the better deal? Explain.

b. What If? Suppose each offer were for 1 year. Would that change your answer? Explain.

c. Make a Conjecture Find the difference in monthly rates. Divide the cost of the DiV digital video recorder by the difference and round up to the nearest whole number. What does this quotient represent?

17. Draw Conclusions Two stores have a sale on T-shirts originally priced at $8.50. Yeager’s has a “Buy 2, get 1 free” sale. Gample’s has a 30% off sale. Dirk wants to buy only 2 T-shirts. Which is the better buy for him? Explain your reasoning.

18. Represent Real-World Problems Suppose you are buying books from an online store, and the total price of your books is $39. Orders of $50 or more for eligible items qualify for free shipping. Would you buy more to qualify for free shipping? Or would you check out with only the books you have in your shopping cart? Explain your answer.

422

Unit 7

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16. Analyze Relationships Sandy wants to buy 5 pounds of apples. She has a coupon for $1.00 off for every 3 pounds of apples. She gets to the store and discovers that apples are on sale for $0.75 a pound. Is it cheaper for her to buy 5 pounds or 6 pounds? Explain.

MODULE QUIZ

Ready

Personal Math Trainer

13.1 Calculating Sales and Income Tax

Online Assessment and Intervention

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1. Marcel bought a new hat for $21.99 and 2 pairs of socks for $3.99 each. What is the total price, including a 7.5% sales tax? For 2–3, use the tax table shown. Jennifer computed her taxable income as $24,382 and paid $3,115 in federal withholding.

If line 43 (taxable income is –

And you are single

At least

But less than

Your tax is –

24,250 24,300 24,350

24,300 24,350 24,400

3,216 3,224 3,231

2. How much federal income tax is Jennifer required to pay? 3. Determine whether Jennifer still owes money or will get a refund, and what amount that is.

13.2 Calculating and Comparing Simple and Compound Interest

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4. Two savings accounts each start with a $200 principal and have an interest rate of 5%. One account earns simple interest and the other is compounded annually. Which account will earn more interest over 10 years? How much more?

13.3 Making Purchasing Decisions 5. Brenda wants to buy a sweater that is regularly priced at $27. She can apply one of two coupons, $5 off or 25% off. Which should she use?

ESSENTIAL QUESTION 6. How can you use your knowledge of taxes and simple and compound interest to help you make informed decisions in the real-world?

Module 13

423

Personal Math Trainer

MODULE 13 MIXED REVIEW

Texas Test Prep Selected Response 1. Tela bought a backpack for $34.99 and 3 notebooks for $1.89 each. What is the total price, including a 8% sales tax? A $38.77

C

B $40.66

D $43.91

$41.87

Taylor’s gross monthly pay is $2,500. Use this information for 2–4. 2. Taylor pays 15.6% of his monthly income for federal withholding. How much federal withholding does he pay? A $32.50

C

B $375

D $2,110

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6. Each year on the same day, Lia deposits $225 in an account that earns simple interest at a rate of 4%. How much interest does her account earn after 10 years? A $9

C

B $90

D $495

$234

7. Omar deposits $300 in an account earning 3% interest compounded annually. How much interest will the account earn after 5 years if he makes no withdrawals? A $45

C

B $47.78

D $347.78

$345

$390

A $30.56

C

B $36.25

D $2,536.25

$2,140.56

4. How much does Taylor pay for Social Security, which is 6.2% of his monthly salary? A $130.82

C

B $155

D $2,655

$2,240.82

Gridded Response 8. Carey computed her taxable income as $27,342 and paid $4,127 in federal withholding. Use the tax table to find the amount in dollars Carey will get as a refund. If line 43 (taxable income is –

And you are single

At least

But less than

Your tax is –

27,200 27,250 27,300 27,350

27,250 27,300 27,350 27,400

3,659 3,666 3,674 3,681

5. Kit can purchase a 6-pound item from several different retailers. Which is the best buy?

. 0

0

0

0

0

0

1

1

1

1

1

1

2

2

2

2

2

2

3

3

3

3

3

3

4

4

4

4

4

4

Pay at a local store with a regular price of $32.95 and a $5-off coupon.

5

5

5

5

5

5

6

6

6

6

6

6

D Pay at a local store with a regular price

7

7

7

7

7

7

8

8

8

8

8

8

9

9

9

9

9

9

A Buy online for $24 plus pay shipping

and handling costs of $0.79 per pound. B Buy online for $25 plus pay shipping

and handling costs of $0.49 per pound. C

of $40 on sale for 25% off.

Unit 7

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3. How much does Taylor pay for Medicare, which is 1.45% of his monthly salary?

424

Online Assessment and Intervention

Planning Your Future ?

MODULE

14

LESSON 14.1

ESSENTIAL QUESTION

Personal Budgets 7.13.B

How can you use mathematics to plan for a successful financial future?

LESSON 14.2

Planning a Budget 7.13.D

LESSON 14.3

Constructing a Net Worth Statement

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7.13.C

Real-World Video

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Creating and sticking to a household budget is an important part of smart spending and saving. Having a plan for how much you can spend on various expenses helps you control your debt.

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Math On the Spot

Animated Math

Personal Math Trainer

Go digital with your write-in student edition, accessible on any device.

Scan with your smart phone to jump directly to the online edition, video tutor, and more.

Interactively explore key concepts to see how math works.

Get immediate feedback and help as you work through practice sets.

425

Are YOU Ready? Personal Math Trainer

Complete these exercises to review skills you will need for this chapter.

Compare and Order Decimals EXAMPLE

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Online Assessment and Intervention

tens ones · tenths hundredths thousandths Compare tens: 4 = 4 4

6

·

0

3

8

4

6

·

0

5

1

Compare ones: 6 = 6 Compare tenths: 0 = 0 Compare hundredths: 5 > 3 So, 46.051 > 46.038

Compare. Write > or

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