Gerver R.K., Sgroi R.J. Financial Algebra
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Robert Gerver
Richard Sgroi
Australia • Brazil • Japan • Korea • Mexico • Singapore • Spain • United Kingdom • United States
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© 2011 South-Western, Cengage Learning
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Student Edition ISBN-13: 978-0-538-44967-0
Student Edition ISBN-10: 0-538-44967-5
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Financial Algebra
Robert Gerver and Richard Sgroi
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A Note from the
Financial Algebra Authors
Welcome to an exciting new math course where you will learn to con-
nect algebra to what’s going on in your life. Since you are earning, spending,
saving, and investing now and will be throughout the rest of your life, it’s time
to understand fi nance in mathematical terms and gain confi dence in your abil-
ity to manage money.
By building on your prior knowledge of math concepts from other courses,
Financial Algebra will take you step-by-step through strategies to help you
learn the time value of money, how to evaluate the best cell phone contract,
how to build a business plan by knowing costs, profi ts, and breakeven points,
and much more. The applications-based practice problems use real-life scenar-
ios that have been researched and fi eld-tested by the authors’ students over
many years.
This new algebra-based and technology-oriented book features ten chap-
ters under six fi nancial umbrellas: Investing, Banking, Credit, Income Taxes,
Insurance, and Household Budgeting. It reviews and strengthens your alge-
bra mechanics and problem-solving skills, while at the same time teaches you
selected advanced mathematics topics. For example, Financial Algebra intro-
duces you to piecewise functions, regression, limits, exponential functions,
linear/quadratic systems, and more.
As you embark on life in the 21st century, you will be required to use math-
ematics frequently in your daily life to make crucial decisions that will affect you
and your family’s lifestyle. You will fi nd that Financial Algebra is a fi eld trip from
cover to cover. Please take this journey with us.
Robert Gerver
North Shore High School
Glen Head, New York
Richard Sgroi
Fox Lane High School
Bedford, New York
Robert Gerver, Ph.D. and
Richard Sgroi, Ph.D. are well
known mathematics teachers,
authors, and speakers at
mathematics conferences
throughout the United States.
Over the course of their 30-year
careers, they have developed
teaching methods to unmask
the mysteries of mathemat-
ics with applications to music,
business, fi nance, and practical
living skills.
Dr. Gerver has taught at North Shore High School,
Glen Head, New York, for more than 30 years.
He is a recipient of the Presidential Award for
Excellence in Mathematics Teaching.
Dr. Sgroi teaches at Fox Lane High School,
Bedford, New York. He is formerly assistant
professor of mathematics and mathematics
education at the State University of New York
at New Paltz.
iii
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iv
Financial Algebra Reviewers
Ida Baird
Mathematics Teacher and
Co-Department Chair
Richland High School
Richland, Washington
Margaret L. Bartels
Mathematics Teacher
Broward County, Florida
Elaine M. Bell
Mathematics Teacher
Hartland High School
Hartland, Michigan
Kevin R. Bowdler
Mathematics Teacher
Loveland High School
Loveland, Ohio
Sharon Deiling
Math Integration Specialist
Dauphin County Tech School
Harrisburg, Pennsylvania
Lori DeWitt
Mathematics Teacher
Space Coast Jr./Sr. High School
Brevard County, Florida
Robert M. Early
Mathematics Teacher
Cocoa Beach Jr./Sr. High School
Cocoa Beach, Florida
Joshua Folb
Mathematics Teacher
Arlington Public Schools
Arlington, Virginia
Elaine Gottschalk
Mathematics Teacher
Notre Dame Prep School
Towson, Maryland
Katie Gruenwald
Mathematics Teacher
Madison Central High School
Richmond, Kentucky
Marie B. Jump
Mathematics Teacher
Lloyd Memorial High School
Erlanger, Kentucky
Robert Kimball
Consultant
Wake Technical Community College
Raleigh, North Carolina
Sherry M. Larson
Mathematics and Science Teacher
Lennox High School
Lennox, South Dakota
Linda Lebovitz
Mathematics Teacher
Viera High School
Viera, Florida
Greg Malkin
Mathematics Teacher
University School
Cleveland, Ohio
Tara L. McCasland
Mathematics Teacher
Kankakee High School
Kankakee, Illinois
Jodi Meyer
Mathematics Teacher
St. Margaret’s School
Tappahannock, Virginia
Ronald G. Noble
State Coordinator, Washington
Applied Math Council
Colville High School
Colville, Washington
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v
Cindy Percival
Mathematics Teacher
Roosevelt High School
Des Moines, Iowa
Peter G. Rudowski
Mathematics Teacher
Mason City Schools
Mason, Ohio
Melanie Scott, NBCT
Mathematics Teacher
Madison Central High School
Richmond, Kentucky
Traci L. Stiles
Mathematics Teacher
Merritt Island High School
Merritt Island, Florida
Andy Wait
Math Department Chair
San Luis High School
San Luis, Arizona
Terri L. Wargo
Mathematics Teacher
Palm Bay High School
Melbourne, Florida
Sharon S. Whitehead, PhD
Independent Mathematics Consultant
Arizona State University
Arizona Department of Education
Mesa, Arizona
Matt Wheeler
Math Department Chair
Mesquite High School
Gilbert, Arizona
Comstock/Getty Images
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vi
Contents
Chapter 1 The Stock Market 2
1-1 Business Organization 4
1-2 Stock Market Data 9
1-3 Stock Market Data Charts 16
1-4 Simple Moving Averages 22
1-5 Stock Market Ticker 29
1-6 Stock Transactions 35
1-7 Stock Transaction Fees 40
1-8 Stock Splits 45
1-9 Dividend Income 51
Chapter 2 Modeling a Business 62
2-1 Interpret Scatterplots 64
2-2 Linear Regression 70
2-3 Supply and Demand 75
2-4 Fixed and Variable Expenses 80
2-5 Graphs of Expense and Revenue
Functions 86
2-6 Breakeven Analysis 91
2-7 The Profi t Equation 97
2-8 Mathematically Modeling
a Business 103
Chapter 3 Banking Services 114
3-1 Checking Accounts 116
3-2 Reconcile a Bank Statement 123
3-3 Savings Accounts 131
3-4 Explore Compound Interest 137
3-5 Compound Interest Formula 143
3-6 Continuous Compounding 150
3-7 Future Value of Investments 156
3-8 Present Value of Investments 161
MATH TOPICS
Candlestick chart
Fractions, decimals, and percents
Linear equation
Literal equation
Mean – arithmetic average
Percent increase and decrease
Ratio and proportion
Read, interpret, and create bar and line graphs
Simple moving average
Spreadsheets and formulas
MATH TOPICS
Causal relationship
Functions - domain and range
Linear equation – slope-intercept form
Linear regression
Parabola – vertex and axis of symmetry
Quadratic formula
Scatterplots and correlation
Spreadsheets and formulas
Transitive property of dependence
MATH TOPICS
Exponential functions
Exponential base (e)
Exponential growth and decay
Formulas
Linear equations and inequalities
Limits
Order of operations
Recursive and iterative thinking: patterns,
growth, decline, compound interest
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vii
Chapter 4 Consumer Credit 172
4-1 Introduction to Consumer Credit 174
4-2 Loans 181
4-3 Loan Calculations and Regression 187
4-4 Credit Cards 193
4-5 Credit Card Statement 200
4-6 Average Daily Balance 206
Chapter 5 Automobile Ownership 216
5-1 Classifi ed Ads 218
5-2 Buy or Sell a Car 224
5-3 Graph Frequency Distributions 231
5-4 Automobile Insurance 238
5-5 Linear Automobile Depreciation 245
5-6 Historical and Exponential
Depreciation 252
5-7 Driving Data 259
5-8 Driving Safety Data 268
5-9 Accident Investigation Data 274
MATH TOPICS
Cubic regression
Exponential growth and decay
Linear equations and inequalities
Linear regression
Measures of central tendency
Natural logarithm, base e
Percents
Quadratic regression
Spreadsheets and formulas
MATH TOPICS
Circles (radius, diameter, chord)
Distance Formula
Exponential growth and decay
Linear equations and inequalities
Linear and exponential functions
Measures of central tendency
Metric System
Natural logarithm
Percents and Proportions
Piecewise functions
Range
Read and interpret data: frequency tables,
stem-and-leaf plots, box plots
Quartiles
Straight line equations (depreciation)
Slope, slope-intercept form
Square root equations
Spreadsheets and formulas
Systems of linear equations and inequalities
in two variables
iStock
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viii
Chapter 6 Employment Basics 288
6-1 Look for Employment 290
6-2 Pay Periods and Hourly Rates 296
6-3 Commissions, Royalties, and
Piecework Pay 303
6-4 Employee Benefi ts 310
6-5 Social Security and Medicare 316
Chapter 7 Income Taxes 326
7-1 Tax Tables, Worksheets, and
Schedules 328
7-2 Modeling Tax Schedules 335
7-3 Income Statements 344
7-4 Forms 1040EZ and 1040A 352
7-5 Form 1040 and Schedules A and B 365
Chapter 8 Independent Living 382
8-1 Find a Place to Live 384
8-2 Read a Floor Plan 393
8-3 Mortgage Application Process 401
8-4 Purchase a Home 411
8-5 Rentals, Condominiums,
and Cooperatives 422
MATH TOPICS
Cusps
Piecewise functions
Exponential functions
Graphs
Linear functions
Literal expressions
Measures of central tendency
Percent discount
Spreadsheets and formulas
MATH TOPICS
Area and scale factor
Area of irregular regions
Bar graphs
Exponential regression
Greatest integer function
Literal expressions
Monte Carlo method
Probability
Rational and exponential equations
Scale drawings
Scatterplots and linear regression
Spreadsheets and formulas
Systems of linear equations and inequalities in
two variables
MATH TOPICS
Cusps
Domains
Linear equations and inequalities
Literal expressions
Percent
Piecewise functions
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ix
Chapter 9 Planning for Retirement 436
9-1 Retirement Income from Savings 438
9-2 Social Security Benefi ts 447
9-3 Pensions 456
9-4 Life Insurance 464
Chapter 10 Prepare a Budget 480
10-1 Utility Expenses 482
10-2 Electronic Utilities 489
10-3 Charting a Budget 496
10-4 Cash Flow and Budgeting 508
Appendix-2008 Tax Table 526
Glossary 539
Index 552
MATH TOPICS
Collect, organize, and interpret data
Domain
Expected value
Exponential equations
Greatest integer functions
Histogram
Inequalities
Literal expressions
Measures of central tendency
Percent increase
Probability
Rational equations
Spreadsheets and formulas
Slope-intercept forms
MATH TOPICS
Circle (sectors, central angel)
Cusp
Domain
Fractions, decimals, and ratios
Greatest integer function
Linear equations and inequalities
Literal expressions
Matrices
Piecewise functions
Proportions
Rational and exponential equations
Read and interpret data: line graphs,
bar graphs, circle graphs
Slope and graphing linear functions
Spreadsheets and formulas
Systems of equations
Volume
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