Business and Financial Mathematics introduces students to the ideas, concepts, and applications of the mathematics of business and finance.  Topics include the mathematics of merchandising, cost-volume-profit analysis, simple and compound interest, annuities, loans, bonds, and business investment decisions.  

The book is written at an introductory level, designed for students studying business, finance, or other related areas.  

The text emphasizes the understanding and application of technology, in the form of a financial calculator, to solve problems, but some knowledge of algebra is required.

Contents Page: 

Acknowledgements

About this Book

Changes from Adapted Sources

I. Mathematics of Merchandising

1.1 Discounts

1.2 Invoices, Terms of Payments, and Cash Discounts

1.3 Markup

1.4 Markdown

1.5 Working with Discounts, Markup, and Markdown

1.6 Review Exercises

1.7 Chapter Summary

II. Cost-Volume-Profit Analysis

2.1 Cost-Volume-Profit Analysis Terminology

2.2 Revenue and Cost Functions

2.3 Contribution Margin

2.4 Contribution Rate

2.5 Review Exercises

2.6 Chapter Summary

III. Simple Interest and Its Applications

3.1 Simple Interest: Principal, Rate, Time

3.2 Simple Interest: Maturity Value

3.3 Savings Accounts And Short-Term Guaranteed Investment Certificates

3.4 Treasury Bills and Commercial Papers

3.5 Demand Loans

3.6 Review Exercises

3.7 Chapter Summary

IV. Compound Interest

4.1 Compound Interest Terminology

4.2 Calculating the Future Value

4.3 Calculating the Present Value

4.4 Equivalent Payments

4.5 Calculating the Interest Rate

4.6 Calculating the Term

4.7 Effective and Equivalent Interest Rates

4.8 Review Exercises

4.9 Chapter Summary

V. Annuities

5.1 Fundamentals of Annuities

5.2 Future Value of Annuities

5.3 Present Value of Annuities

5.4 Calculating the Payment

5.5 Calculating the Term of an Annuity

5.6 Calculating the Interest Rate for an Annuity

5.7 Deferred Annuities

5.8 Perpetuities

5.9 Review Exercises

5.10 Chapter Summary

VI. Loans and Mortgages

6.1 Amortization Schedules

6.2 Calculating the Principal and Interest Components of a Loan Payment

6.3 Calculating the Final Payment

6.4 Mortgages

6.5 Review Exercises

6.6 Chapter Summary

VII. Bonds and Sinking Funds

7.1 Bond Terminology

7.2 Calculating the Purchase Price of a Bond on an Interest Payment Date

7.3 Calculating the Yield Rate

7.4 Bond Schedules

7.5 Quotation of Bonds

7.6 Sinking Funds

7.7 Review Exercises

7.8 Chapter Summary

VIII. Business Investment Decisions

8.1 Net Present Value

8.2 Internal Rate of Return

8.3 Review Exercises

8.4 Chapter Summary

Versioning History

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Business Math: a step-by-step handbook was written to meet the needs of a twenty-first century student. It takes a systematic approach to helping students learn how to think and centers on a structured process termed the PUPP Model (Plan, Understand, Perform, and Present). This process is found throughout the text and in every guided example to help students develop a step-by-step problem-solving approach.

This textbook simplifies and integrates annuity types and variable calculations, utilizes relevant algebraic symbols, and is integrated with the Texas Instruments BAII+ calculator. It also contains structured exercises, annotated and detailed formulas, and relevant personal and professional applications in discussion, guided examples, case studies, and even homework questions.

Relevance:

As educators, we constantly hear, “…and when will I ever use that in my life?” This textbook demonstrates to students both personal and professional applications in discussions, guided examples, case studies, and even their homework questions:

1. On a personal level, students are shown realistic scenarios, companies, and products that they commonly are exposed to. It is always easier to learn something when students can relate to it.

2. On a professional level, this textbook demonstrates business situations in different business fields so that students can see applicability regardless of their chosen career path. Whether students are planning on becoming accountants or marketers, there are applications to be found in this textbook.

Table of Contents:

Licensing

Textbook Features

A Note on Rounding Rules

About The Author

1: Succeeding in Business Mathematics (How To Use This Textbook)

• 1.0: Introduction

• 1.1: What Is Business Math?

• 1.2: How Can I Use The Features Of This Book To My Advantage?

• 1.3: Where Do We Go From Here?

• 1.4: Rounding Rules (Appendix 1)

• 1.E: Succeeding in Business Mathematics (Exercises)

2: Back To The Basics (Shoulder Check)

• 2.0: Introduction

• 2.1: Order of Operations (Proceed In An Orderly Manner)

• 2.2: Fractions, Decimals, and Rounding (Just One Slice Of Pie, Please)

• 2.3: Percentages (How Does It All Relate?)

• 2.4: Algebraic Expressions (The Pieces Of The Puzzle)

• 2.5: Linear Equations - Manipulating and Solving (Solving the Puzzle)

• 2.6: Natural Logarithms (How Can I Get That Variable Out of the Exponent?)

• 2.S: Summary

• 2.E: Back To The Basics (Exercises)

3: General Business Management Applications (Get Your Motor Running)

• 3.0: Introduction

• 3.1: Percent Change (Are We Up Or Down?)

• 3.2: Averages (What Is Typical?)

• 3.3: Ratios, Proportions, and Prorating (It Is Only Fair)

• 3.S: Summary

• 3.CS: Case Study (Forecasting Future Sales)

• 3.E: General Business Management Applications (Exercises)

4: Human Resources and Economic Applications (It's All about the People)

• 4.0: Introduction

• 4.1: Gross Earnings (Off to Work You Go)

• 4.2: Personal Income Tax (The Taxman Taketh)

• 4.3: Indexes (The Times Are Changing)

• 4.S: Summary

• 4.CS: Case Study-Payroll Planning

• 4.E: Human Resources and Economic Applications (Exercises)

5: Marketing and Accounting Fundamentals (Keeping Your Nose above Water)

• 5.0: Introduction

• 5.1: Cost-Revenue-Net Income Analysis (Need to Be in the Know)

• 5.2: Break-Even Analysis (Sink or Swim)

• 5.S: Marketing and Accounting Fundamentals (Summary)

• 5.CS: Case Study: Forecasting the Impact of Revenue and Cost Changes

• 5.E: Marketing and Accounting Fundamentals (Exercises)

6: Marketing Applications (What Is It Going to Cost Me?)

• 6.0: Introduction to Marketing Applications

• 6.1: Figuring Out the Cost - Discounts (How Much?)

• 6.2: Markup- Setting the Regular Price (Need to Stay in Business)

• 6.3: Markdown: Setting the Sale Price (Everybody Loves a Sale)

• 6.4: Merchandising (How Does It All Come Together?)

• 6.S: Summary

• 6.CS: Case Study (Making a Profitable Product Selection)

• 6.E: Marketing Applications (Exercises)

7: Accounting Applications

• 7.0: Introduction

• 7.1: Sales Taxes

• 7.2: Property Taxes

• 7.3: Exchange Rates and Currency Exchange

• 7.4: Invoicing - Terms of Payment and Cash Discounts

• 7.S: Summary

• 7.CS: Case Study - Completing Summary Financial Reports

• 7.E: Accounting Applications (Exercises)

8: Simple Interest- Working With Single Payments and Applications

• 8.0: Introduction

• 8.1: Principal, Rate, Time

• 8.2: Moving Money Involving Simple Interest

• 8.3: Savings Accounts And Short-Term GICs

• 8.4: Application - Promissory Notes

• 8.5: Application - Loans

• 8.6: Application - Treasury Bills and Commercial Papers

• 8.S: Summary

• 8.CS: Case Study - Managing A Company's Investments

• 8.E: Simple Interest- Working With Single Payments and Applications (Exercises)

9: Compound Interest- Working With Single Payments

• 9.0: Introduction

• 9.1: Compound Interest Fundamentals

• 9.2: Determining the Future Value

• 9.3: Determining the Present Value

• 9.4: Equivalent Payments

• 9.5: Determining the Interest Rate

• 9.6: Equivalent and Effective Interest Rates

• 9.7: Determining the Number of Compounds

• 9.S: Summary

• 9.CS: Case Study - Exploring Different Sources Of Compound Financing

• 9.E: Compound Interest- Working With Single Payments (Exercises)

10: Compound Interest- Applications Involving Single Payments

• 10.0: Introduction

• 10.1: Application - Long-Term GICs

• 10.2: Application - Long-Term Promissory Notes

• 10.3: Application - Savings Bonds

• 10.4: Application - Strip Bonds

• 10.5: Application - Inflation, Purchasing Power, and Rates Of Change

• 10.S: Summary

• 10.CS: Case Study - How Much Interest Is Really Earned?

• 10.E: Compound Interest- Applications Involving Single Payments (Exercises)

11: Compound Interest- Annuities

• 11.0: Introduction

• 11.1: Fundamentals of Annuities

• 11.2: Future Value Of Annuities

• 11.3: Present Value Of Annuities

• 11.4: Annuity Payment Amounts

• 11.5: Number Of Annuity Payments

• 11.6: Annuity Interest Rates

• 11.S: Summary

• 11.CS: Case Study - Developing Product Payment Plans

• 11.E: Compound Interest- Annuities (Exercises)

12: Compound Interest- Special Applications Of Annuities

• 12.0: Introduction

• 12.1: Deferred Annuities

• 12.2: Constant-Growth Annuities

• 12.3: Perpetuities

• 12.4: Leases

• 12.5: Application - How To Purchase A Vehicle

• 12.6: Application - Planning Your RRSP

• 12.S: Summary

• 12.CS: Case Study - Should You Go On Strike?

• 12.E: Compound Interest- Special Applications Of Annuities (Exercises)

13: Understanding Amortization and its Applications

• 13.0: Introduction

• 13.1: Calculating Interest and Principal Components

• 13.2: Calculating the Final Payment

• 13.3: Amortization Schedules

• 13.4: Special Application - Mortgages

• 13.S: Summary

• 13.CS: Case Study - Cash Or Credit?

• 13.E: Understanding Amortization and its Applications (Exercises)

14: Bonds and Sinking Funds

• 14.0: Introduction

• 14.1: Determining the Value of a Bond

• 14.2: Calculating a Bond’s Yield

• 14.3: Sinking Fund Schedules

• 14.4: Debt Retirement and Amortization

• 14.S: Summary

• 14.CS: Case Study - Financing An Acquisition Through Bonds

• 14.E: Bonds and Sinking Funds (Exercises)

15: Making Good Decisions

• 15.0: Introduction

• 15.1: Net Present Value

• 15.2: Other Measures For Making Decisions

• 15.S: Summary

• 15.CS: Case Study - Choosing a New Supplier

• 15.E: Making Good Decisions (Exercises)

16: Appendices

• 16.1: Exercise Solutions (Appendix A)

• 16.2: Bibliography

• 16.3: Rounding Rules

• 16.4: Formula Sheet

• 16.NS: Notation Summary

Index

Glossary

Detailed Licensing

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Data analytics is a rapidly evolving field. In today’s labour market, knowing how to acquire, process, and interpret large amounts of data to make optimal decisions is crucial for many professionals, especially those in business and engineering. This open textbook, “a new online course” if you will, focuses on three key concept areas: data acquisition, data processing, and decision-making models. 

In this course, students will be able to develop advanced knowledge and skills to acquire related data for operations of business or projects; apply quantitative literacy skills such as statistics and machine learning; and use predictive or prescriptive modeling to make timely, actionable, and meaningful decisions..

Contents (summary):

Introduction

Acknowledgements

Accessibility Statement

Adopting or Adapting the Book

1. Introduction to Data Analytics and Decision Making

1.1 Introduction to Data Analytics and Decision Making

1.3 Careers in Data Analytics

1.4 Data Types, Formats and Repositories

1.5 Data Technologies: Big Data and Cloud Computing

1.6 Stages of Data Analytics

1.7 Predictive Analytics: Statistical Learning & Machine Learning

1.8 Prescriptive Analytics

2. Descriptive Analytics

2.1 Descriptive Analytics

2.2 Data Visualization

2.3 Data Summarization

Assignment 1

3. Predictive Analytics

3.1 Predictive Analytics

3.2 Regression

3.3 Multiple Linear Regression

3.4 Non-Linear Relationships/Polynomial Regression

3.5 Logistic Regression

Assignment 2

3.6 K-Nearest Neighbours

3.7 Cross Validation

3.8 Resampling

3.9 Feature Selection

4. Prescriptive Analytics

4.1 Prescriptive Analytics

4.2 Minimum Cost Network Flow Problem (MCNFP)

4.3 Routing

4.4 Simulation

4.5 Investment Management

4.6 Stochastic Decision Tree Analysis

Assignment 3

4.7 Revenue Management

Assignment 4

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Contemporary Mathematics is designed to meet the scope and sequence requirements for a liberal arts mathematics course. This resource provides stand-alone sections with a focus on showing relevance in the features as well as the examples, exercises, and exposition. Contemporary Mathematics integrates technology applications, projects, and highlights a diverse group of contributors to mathematics, statistics, and related fields.

Contents (summary):

• Ch. 1. Sets

• Ch. 2. Logic

Introduction

2.1 Statements and Quantifiers

2.2 Compound Statements

2.3 Constructing Truth Tables

2.4 Truth Tables for the Conditional and Biconditional

2.5 Equivalent Statements

2.6 De Morgan’s Laws

2.7 Logical Arguments

Chapter Summary

• Ch. 3. Real Number Systems and Number Theory

• Ch. 4. Number Representation and Calculation

• Ch. 5. Algebra

• Ch. 6. Money Management

Introduction

6.1 Understanding Percent

6.2 Discounts, Markups, and Sales Tax

6.3 Simple Interest

6.4 Compound Interest

6.5 Making a Personal Budget

6.6 Methods of Savings

6.7 Investments

6.8 The Basics of Loans

6.9 Understanding Student Loans

6.10 Credit Cards

6.11 Buying or Leasing a Car

6.12 Renting and Homeownership

6.13 Income Tax

Chapter Summary

• Ch. 7. Probability

• Ch. 8. Statistics

• Ch. 9. Metric Measurement

Introduction

9.1 The Metric System

9.2 Measuring Area

9.3 Measuring Volume

9.4 Measuring Weight

9.5 Measuring Temperature

Chapter Summary

• Ch. 10. Geometry

• Ch. 11. Voting and Apportionment

Introduction

11.1 Voting Methods

11.2 Fairness in Voting Methods

11.3 Standard Divisors, Standard Quotas, and the Apportionment Problem

11.4 Apportionment Methods

11.5 Fairness in Apportionment Methods

Chapter Summary

• Ch. 12. Graph Theory

Introduction

12.1 Graph Basics

12.2 Graph Structures

12.3 Comparing Graphs

12.4 Navigating Graphs

12.5 Euler Circuits

12.6 Euler Trails

12.7 Hamilton Cycles

12.8 Hamilton Paths

12.9 Traveling Salesperson Problem

12.10 Trees

Chapter Summary

• Ch. 13. Math and Liberal Arts

Introduction

13.1 Math and Art

13.2 Math and the Environment

13.3 Math and Medicine

13.4 Math and Music

13.5 Math and Sports

Chapter Summary

Appendix A Co-Req Appendix: Integer Powers of 10

Answer Key

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This text has been adapted from the following resources:

• Business Math: A Step-by-Step Handbook (2018, Revision A) by J. Olivier, under a CC BY-NC-SA License.

• Business Precalculus by D. Lippman, under a CC BY-SA 3.0 United States License.

Summarised Contents Page: 

Acknowledgements

Attributions

I. Main Body

1. Review of the Basics

2. General Business Management Applications

3. Human Resources and Economic Applications

4. Marketing Applications

5. Accounting Applications

6. Simple Interest

7. Functions and Lines

8. Systems of Equations and Linear Programming

9. Polynomial and Rational Functions

10. Exponential and Logarithmic Functions

11. Finance

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Introductory Business Statistics 2e aligns with the topics and objectives of the typical one-semester statistics course for business, economics, and related majors. The text provides detailed and supportive explanations and extensive step-by-step walkthroughs. The author places a significant emphasis on the development and practical application of formulas so that students have a deeper understanding of their interpretation and application of data. Problems and exercises are largely centered on business topics, though other applications are provided in order to increase relevance and showcase the critical role of statistics in a number of fields and real-world contexts.

The second edition retains the organization of the original text. Based on extensive feedback from adopters and students, the revision focused on improving currency and relevance, particularly in examples and problems.

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This textbook was created to support the study of key mathematical concepts and skills among future occupational and public health professionals. Specifically, it contains material adapted from multiple existing resources on college- and university-level mathematics. The primary intended use of the textbook is for the course POH103 “Data Management” at Ryerson University, but it could be used or adapted to other settings.

The material is designed for first-year undergraduate occupational and public health students with different backgrounds in mathematics. The material is intended to prepare students for more advanced quantitative courses in biostatistics, epidemiology, and risk assessment, among others.

Table of contents:

Chapter 1: Algebra Review

1.1. Introduction to Algebra

1.2. Equations

1.3. Measurement Systems

1.4. Ratios, Rates, and Percent

1.5. Exponents and Scientific Notation

1.6. Practice question answers

Chapter 2: Linear Equations and Graphs

2.1. Graphing a Linear Equation

2.2. Slope of a Line

2.3. Equation of a Line

2.4. Applications

2.5. Practice question answers

Chapter 3: Introduction to Functions

3.1. Introduction to Functions

3.2. Domain and Range

3.3. Rates of Change and Behaviour of Graphs

3.4. Quadratic Functions

3.5. Practice question answers

Chapter 4: Exponential and Logarithmic Functions

4.1. Exponential Functions

4.2. Logarithmic Functions

4.3. Exponential and Logarithmic Models

4.4. Practice question answers

Chapter 5: Sets and Counting

5.1. Set Theory and Venn Diagrams

5.2. Multiplication Axiom

5.3. Permutations

5.4. Combinations

5.5. Practice question answers

Chapter 6: Probability - Part 1

6.1. Sample Spaces and Probability

6.2. Mutually Exclusive Events and the Addition Rule

6.3. Probability Using Tree Diagrams and Combinations

6.4. Conditional Probability

6.5. Independent Events

6.6. Practice question answers

Chapter 7: Probability - Part 2

7.1. Binomial Probability

7.2. Bayes' Formula

7.3. Expected Value and Tree Diagrams

7.4. Markov Chains

    7.5. Practice question answers

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Our environmental, economic, and social systems are currently facing a host of challenges, which if left unaddressed will have significant implications for the world in which we live. Tackling these challenges will require better-informed decision-making, which in turn requires models that are designed and developed with sustainable development considerations and objectives in mind. To support this need for better-informed decision making, this book brings together the insights and expertise of a dozen expert modellers and policy analysts, who completed this project on modelling for sustainable development in June 2019 using the "Book Sprints" method. 

This practical book:

• Outlines the different modelling approaches available; 

• Describes why model design and development matters for sustainable development; and 

• Explains how these models can contribute to decision-making processes.

The book is designed for decision-makers, model commissioners, model developers, model users, and students specializing in modelling and/or the different aspects of sustainable development. 

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This is an open access book discusses readers to various methods of modeling plans and policies that address public sector issues and problems. Written for public policy and social sciences students at the upper undergraduate and graduate level, as well as public sector decision-makers, it demonstrates and compares the development and use of various deterministic and probabilistic optimization and simulation modeling methods for analyzing planning and management issues. These modeling tools offer a means of identifying and evaluating alternative plans and policies based on their physical, economic, environmental, and social impacts. 

Learning how to develop and use the mathematical modeling tools introduced in this book will give students useful skills when in positions of having to make informed public policy recommendations or decisions.

Contents page:

Front Matter

• Analyzing Public Policy Decisions

• Public Sector Systems

• Creating Models

• Modeling Examples and Solutions

• Models for Managing Money

• Solving Models Using Excel

• Discrete Optimization Modeling

• Linear Optimization Modeling

• Some Linearization Methods

• Solving Models Using Calculus

• Lagrangian Models

• Dealing with Uncertainty

• Modeling Stochastic Processes

• Chance Constrained and Monte Carlo Modeling

• Simulation Modeling

• Multi-criteria Analyses

• Fuzzy Optimization

• Conclusion

Back Matter

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Keywords:

Public systems planning; Public management; Operations research; Models for policy analyses; Public evaluation; Policy Analysis; Public policy analysis; Linear Optimization Modeling; Discrete Optimization Modeling; Lagrangian Models; Simulation Modeling

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