Steven J. Wilson
Professor of Mathematics
Johnson County Community College

(1st edition, 2001. 2nd edition, 2006.)

3rd edition, 2012.
print ISBN: 978-1-4652-0377-9
e-book ISBN: 978-1-4652-0873-6

Preface

The third edition of Business Math: Using Percents is designed for a one-semester post-arithmetic college level course in Business Mathematics. Major features of the text include:

• emphasis on the use of percentages in business
• the use of non-algebraic methods throughout the text
• the use of financial calculators for compound interest and annuity problems
• a web site containing additional calculator and current tax information

This course emphasizes the use of percentages in business. After an introduction to percents, topics include payroll, retailing, the value of assets, simple and compound interest, and the time value of money.

This textbook assumes that a student is proficient in the operations of elementary arithmetic (fractions and decimals). Chapter 1 is provided as a review of some of those operations needed in this course. Algebra is neither required as a prerequisite, nor are algebraic concepts taught in this text. Non-algebraic methods are used throughout. This text is not designed to be an applied pre-algebra course.

Upon completion of a Business Mathematics course using this textbook, the student should be able to:

• understand both the business concepts and the mathematics concepts presented
• apply knowledge of business math concepts in problem solving situations
• accurately compute values of business math quantities
• interpret results in the specific application, and recognize the implications of the results
• interpret results in a historical context

This text endeavors to present business mathematics as an application of a very few mathematical topics, used in many different situations. Most business mathematics topics are applications of percents. Basic techniques in the use of percentages are presented in chapter 2. Business math topics presented in the later chapters will use these basic techniques. We encourage students to recognize the similarities in the different business math topics, rather than offering a plethora of recipes for many different contexts. Therefore, only a minimal number of broadly applicable formulas are used throughout.

There are several major changes in the third edition. Tax rates and information (sections 3.3-3.5) are once again more current. The material on depreciation (sections 5.3 and 5.4) has been rearranged, so that the commonalities and differences in the types of depreciation method are emphasized. The Actuarial Method for applying loan payments has been included (section 6.6) and compared with the U.S. Rule. The material on compound interest and annuities (chapters 7 and 8) has been completely reorganized, in the recognition that the distinctions made for the existence of payments is rather artificial when financial calculators are employed. This ahs allowed us to present the basic instruction of the different TVM types in chapter 7, and discuss some more advanced topics in finance in a unified fashion in chapter 8. And there have been a host of smaller changes as well.

Technology is prevalent in business settings, and it is our desire that students be able to use the available technology. For problems involving the time value of money (chapters 7 and 8), we recommend the use of a financial calculator. Current prices are less than \$30 for the simplest models, which are completely adequate for this course. No particular brand or model of financial calculator is necessary. The focus of the text is on setting up the problems and identifying the variables, not on the keystrokes of the calculator.

It is possible to use this text without a financial calculator, though we do not recommend that approach. The variables still need to be identified if algebraic formulas or tables are used. We do provide the algebraic formulas in the appendix, but those who wish to use tables will have to obtain them from another source. Tables are very limiting, in that each interest rate requires a different table, so a set of tables can never be complete. Algebraic methods are certainly superior to tables, in that every problem can be turned into an algebraic equation. However, solving the algebraic equation for the interest rate presents obstacles which most students at this level find insurmountable. The financial calculator avoids these difficulties.

The exercises of each section are graded by difficulty. One-star exercises provide routine practice of the basic mathematical computations needed. Two-star exercises generally provide routine applications of business math. Three-star exercises may combine multiple ideas, be at a more difficult level, require a fair amount of time to complete, or ask the student to discuss implications of various situations. We believe every business math student should become proficient in solving two-star problems.

One of the most annoying features of any business mathematics book is the speed at which business math material becomes dated. To partially alleviate this problem, we have made available a web site where current payroll tax information can be found. We have also provided some information about specific financial calculators on this web site. Point your browser to http://www.milefoot.com/math/businessmath/.

Acknowledgments

The author has taught business math at Johnson County Community College for over 20 years, and has long felt the need for a textbook in line with the goals of the course as taught at JCCC. Encouraged by other colleagues in the same situation, he availed himself of a sabbatical opportunity offered by the college to write such a textbook. The author would like to express his sincere appreciation to the Board of Trustees of JCCC for granting sabbatical leave during the spring of 1999 which made this textbook possible. Special thanks for their comments and suggestions also go to Jeff Frost and Libby Holmgren, my colleagues in the JCCC mathematics department, and to the students from spring 2000, fall 2000, and spring 2001, who tested the preliminary edition. Additional thanks are due to colleagues and students too numerous to mention for their comments, corrections, and suggestions over the succeeding years. Their input has helped make the previous second edition (which appeared in 2006) and this current edition a substantial improvement over the first.

1. Fundamentals
1.1 Numbers
1.2 Operations
1.3 Graphs
1.4 Averages
1.5 Proportions

2. Percents
2.1 Interpretation of Percents
2.2 Percent Conversions
2.3 Basic Percent Problems
2.4 Percent Change
2.5 Compounding of Percents

3. Payroll
3.1 Salaries and Wages
3.2 Commission and Piecework
3.3 FICA and FUTA
3.4 Withholding for Income Tax
3.5 After Taxes

4. Retailing
4.1 Profitability
4.3 Cash Discounts
4.4 Markups
4.5 Shrinkage
4.6 Markdowns
4.7 Sales Taxes
4.8 Income Statements

5. Asset Values
5.1 Balance Sheets
5.2 Inventory
5.3 Basic Depreciation
5.4 Accelerated Depreciation
5.5 Ratio Analysis

6. Simple Interest
6.1 The Interest Formula
6.2 Finding Principal, Rate, or Time
6.4 Discount Interest
6.5 Rates
6.6 Applying Loan Payments

7. Time Value of Money
7.1 TVM Variables
7.2 Lump Sum Deposits
7.3 Savings Plans
7.4 Savings Withdrawals
7.5 Loans

8. Financial Issues
8.1 Total Interest
8.2 Effective Rates and the APR
8.3 Rates of Return and APY
8.4 Present Worth
8.5 Effects of Inflation
Appendices
Withholding Tax Tables
Table of Days
Formulas for Compound Interest and Annuities