Preface

PDF Created for Accessibility Purposes OnlyOnline AccessTo register and access the Online Lessons and Online Labs,►► G o to www.intromath.ca and follow the registration instructions.►► W  hen you are prompted to enter an access code, use the code printed below: 24/7 Technical Support [email protected] code can be used only once and cannot be shared. Second toLearn An opportunity to serve the world communitySECOND to Learn is an initiative that has been established by Vretta to provide students withthe exposure and opportunity to support children who cannot afford basic educational resources to pursue their studies. By buying this new textbook, there is a second person who benefits and learns. A portion of the proceeds from the sale of this book will be used to provide a Haitian child in-need with free educational resources such as bags, pencils, and books. To learn more about this initiative visit www.intromath.ca. If you would like to continue supporting this child, send us an email at [email protected] with your contact information.

PDF Created for Accessibility Purposes Only MATHEMATICS OFBUSINESS AND FINANCEOnline Lessons ►► Contain highly engaging and interactive videos that useOnline Labs cutting-edge Cloud Learning technologies. ►► Break down math concepts into logical and intuitive steps that enhance the learning process. ►► Prepare students for upcoming classes, labs, and quizzes through self-study lessons. ►► Contain lessons that are self-paced and are excellent for visual learners. ►► Contain a comprehensive test-bank of real-world problems, which may be used as an assessment tool. ►► Break down every answer into dynamic, step-by-step solutions that include calculator methods of solving problems. ►► Provide unlimited amount of practice through algorithmically generated problems. ►► Contain numerous statistical tools to analyze students’ strengths and weaknesses.

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PDF Created for Accessibility Purposes Only i MATHEMATICS OFBUSINESS AND FINANCE Second Edition Larry Daisley, Seneca College Thambyrajah Kugathasan, Seneca College Diane Huysmans, Fanshawe College

ii PDF Created for Accessibility Purposes Only Copyright © 2014 by Vretta Inc. ISBN 978-1-927737-02-6 Mathematics of Business and Finance, Second Edition Authors: Larry Daisley, Thambyrajah Kugathasan, Diane Huysmans Instructional Design: Charles Anifowose Textbook Editor: Lakshmi Kugathasan Graphic editor: Aleksandar Vozarevic Solution Manual and Test Bank Editors: Phoebe Wu, Arbane Miftari PowerPoint Presentations: Ali Alavi Assistant Editors: Heather Bewley, Caleigh McQuade Textbook Cover and Chapter Cover Design: Stan Lee Expert Advice: TK Academic Consulting Inc., TD Canada Trust Financial Designation Problems: Kaplan-Schweser course materials for Certified Financial Analyst designation Pre-programmed Financial Calculator: Texas Instruments BAII Plus, Sharp EL-738 Turning Technologies’ Student Response System (Clickers) Integrated into Powerpoint Presentations Online Resources: Vretta’s Cloud LearningTM Technologies All rights reserved. Photocopying, recreating, reproducing, storing in any retrieval system, translating, or transmitting in any form or by any means, electronic, digital, graphic, mechanical, physical, audio-video recording, or otherwise of any part of the Mathematics of Business and Finance resources beyond that permitted by the Copyright Act of Canada without the permission of Vretta Inc., the copyright owner, is unlawful. Request for permission or further information should be addressed to the Permissions Department, Vretta Inc. via email at [email protected]. Disclaimer Vretta Inc. has taken complete care to trace the ownership of copyright material contained in these resources. However, if you have any information which would enable us to rectify any reference or credit for subsequent editions and/or identify any errors or omissions which require correction, please email us at [email protected]. The examples, exercises, and cases in the Mathematics of Business and Finance resources are fictitious, unless otherwise stated. Any resemblance to real life people, businesses, organizations, institutions, facts or circumstances is purely coincidental.

PDF Created for Accessibility Purposes Only Preface iiiPreface The Mathematics of Business and Finance resource was created with one primary goal in mind: to help future leaders of business, accounting, marketing, human resources and other disciplines achieve success in their careers. The concepts covered will be beneficial in supporting students to deal with repaying student loans, leasing a car, securing a mortgage, running a business, paying taxes, making investments, and much more. Our team at Vretta has worked to build a resource that will equip our leaders of tomorrow with the core mathematical skills required to perform the day-to-day tasks demanded of them in their field of choice.Blended learning, commonly known as hybrid learning, is a method of combining different learning environments, suchas face-to-face, web-based, and mobile learning. The goal of blended learning is to enhance the learning experience bycatering to different learning styles, including visual, auditory, tactile, and sociological, which are present in the diversegroups of students.To optimize the learning experience, we have leveraged the cutting-edge technologies available to us to providestudents with a highly immersive and engaging learning experience. Realizing that every student learnsdifferently, students are given access to innovative online tools designed to help them master the conceptsusing diverse methods of learning. Students have access to interactive online lessons which give them anunderstanding of the concepts before class. They are also provided with access to the online lab system whichtests them on all the core concepts covered throughout their course. Our aim in building the hybrid tools wasto help overcome the negative perceptions associated with mathematics.At Vretta, we believe that if you learn math, you will live smarter. We truly believe that this blended resource canhelp students achieve a better understanding of the concepts presented and ultimately lead to a better overallquality of life. As students embark on the journey of learning this important subject, we hope that the resourcesfor the Mathematics of Business and Finance provide great value in helping them along the way. Larry, Kuga, Diane, and Team Vretta

iv Brief Contents PDF Created for Accessibility Purposes OnlyBrief ContentsChapter 1 Review of Basic Arithmetic�������������������������������������������������2Chapter 2 Review of Basic Algebra����������������������������������������������������38Chapter 3 Percentages, Percent Changes, and Applications�������������66Chapter 4 Ratios, Proportions, and Applications���������������������������104Chapter 5 Mathematics of Merchandising��������������������������������������140Chapter 6 Linear Systems����������������������������������������������������������������194Chapter 7 Break-Even and Cost-Volume-Profit Analysis���������������218Chapter 8 Simple Interest and Applications�����������������������������������258Chapter 9 Compound Interest���������������������������������������������������������296Chapter 10 Annuities�������������������������������������������������������������������������342Chapter 11 Other Types of Annuities������������������������������������������������406Chapter 12 Amortization of Loans and Mortgages��������������������������430Chapter 13 Bonds and Sinking Funds�����������������������������������������������462Chapter 14 Business Investment Decisions���������������������������������������496 Answer Key����������������������������������������������������������������������518 Glossary���������������������������������������������������������������������������533 Index��������������������������������������������������������������������������������537 Financial Calculator Instructions����������������������������������542 Summary of Formulas����������������������������������������������������544

PDF Created for Accessibility Purposes Only Contents vContentsChapter 1 2 Review of Basic Arithmetic 1.1 Place Value of Numbers and Rounding Numbers.............................................................3 ­Place Value of Whole Numbers.................................................................................3 P­­ lace Value of Decimal Numbers..............................................................................4 R­­ ounding Whole Numbers and Decimals..................................................................5 ­Estimation..................................................................................................................9 Exercises..................................................................................................................101.2 Factors and Multiples......................................................................................................11 P­­ rime Numbers and Composite Numbers.................................................................12 ­Least or Lowest Common Multiple (LCM).................................................................12 Least or Lowest Common Denominator (LCD)..........................................................14 H­ ighest Common Factor (HCF).................................................................................15 Exercises..................................................................................................................151.3 Fractions.........................................................................................................................16 ­Definition of Fractions and Types of Fractions...........................................................16 ­Reciprocal of a Fraction ............................................................................................16 W­­ hole Number as a Fraction.....................................................................................16 ­Converting a Mixed Number into an Improper Fraction.............................................17 ­C­ onverting an Improper Fraction into a Mixed Number.............................................17 ­C­ onverting a Fraction into an Equivalent Fraction ....................................................17 C­ onverting a Fraction to its Decimal Form................................................................18 ­Reducing or Simplifying a Fraction............................................................................18 F­ raction in Lowest (or Simplest) Terms ....................................................................18 Basic Arithmetic Operations with Fractions...............................................................19 Exercises..................................................................................................................211.4 Order of Operations (BEDMAS).......................................................................................23 S­ igned Numbers........................................................................................................24 ­Exponential Notation..................................................................................................25 ­Fractions with Exponents...........................................................................................26 C­ alculator Method to Solve Problems.......................................................................27 Exercises..................................................................................................................281.5 Averages.........................................................................................................................29 ­Simple Arithmetic Average (Arithmetic Mean) ..........................................................29 Weighted Average (Weighted Mean).........................................................................31 Geometric Average (Geometric Mean)......................................................................33 Exercises..................................................................................................................34 Review Exercises...............................................................................................................35 Self-Test Exercises.............................................................................................................36Chapter 2 38 Review of Basic Algebra 2.1 Algebraic Expressions.....................................................................................................39 ­Terminology Used in Algebraic Expressions..............................................................40 Basic Arithmetic Operations with Algebraic Expressions...........................................41 Evaluating Algebraic Expressions..............................................................................44 Factoring Algebraic Expressions with Common Factors...........................................44 Exercises..................................................................................................................45

vi Contents PDF Created for Accessibility Purposes Only2.2 Simple Algebraic Equations and Word Problems.............................................................48 ­Equivalent Equations.................................................................................................48 P­ rinciple of Equations................................................................................................48 Exercises..................................................................................................................522.3 Exponents......................................................................................................................53 ­R­ ules of Exponents and Evaluation of Exponents.....................................................54 F­ ractional Exponents.................................................................................................55 Exercises..................................................................................................................562.4 Logarithms.....................................................................................................................56 Logarithmic Concepts and Relation to Exponents.....................................................56 C­ ommon Logarithms (log).........................................................................................57 N­ atural Logarithms (ln)..............................................................................................57 Rules of Logarithms...................................................................................................58 Exercises..................................................................................................................592.5 Formulas and Applications..............................................................................................60 Exercises..................................................................................................................62 SReelvfi-eTewstEExexercricsieses.s...........................................................................................................................................................................................................................6653Chapter 3 66 Percents, Percent Changes, and Applications 3.1 Percents..........................................................................................................................67 Introduction................................................................................................................67 Relationship Among Percents, Fractions (Ratios), and Decimals ............................67 Calculations Involving Percents.................................................................................69 Exercises..................................................................................................................723.2 Percent Changes.............................................................................................................74 Introduction................................................................................................................74 Exercises..................................................................................................................803.3 Payroll............................................................................................................................82 Introduction................................................................................................................82 Annual Salary............................................................................................................82 Pay Period (Frequency of Payments)........................................................................82 Workweek (Number of Working Hours per Week).....................................................83 Overtime Factor (Used to Calculate Overtime Rate).................................................85 Commissions.............................................................................................................86 Hourly Wages............................................................................................................89 Piecework Rate..........................................................................................................90 Exercises..................................................................................................................913.4 Taxes..............................................................................................................................93 Sales Taxes ..............................................................................................................93 Property Taxes...........................................................................................................95 Exercises..................................................................................................................96 Review Exercises...............................................................................................................98 Self-Test Exercises.............................................................................................................100Chapter 4 104 Ratios, Proportions, and Applications 4.1 Ratios.............................................................................................................................105 Expressing a Ratio of Two Quantities .......................................................................105

PDF Created for Accessibility Purposes Only Contents viiExpressing a Ratio of More than Two Quantities.......................................................105Terms of a Ratio.........................................................................................................105Equivalent Ratio.........................................................................................................105Reducing a Ratio to its Lowest Terms.......................................................................105Order of a Ratio.........................................................................................................107Comparing Quantities of Items That Have the Same Kind of Measure.....................107Comparing Quantities of Items That Have Different Kinds of Measure.....................108Sharing Quantities Using Ratios................................................................................108Unit Rate....................................................................................................................110Exercises .................................................................................................................1104.2 Proportions and Pro-rations............................................................................................112 Proportions................................................................................................................112 Pro-rations.................................................................................................................116 Exercises..................................................................................................................1174.3 Exchange Rates and Applications....................................................................................119 Exchange Rates........................................................................................................119 Buying and Selling Currencies...................................................................................123 Currency Appreciation and Depreciation...................................................................125 Importing Goods from Another Country.....................................................................126 Exercises..................................................................................................................1274.4 Index Numbers and Applications....................................................................................129 Index Numbers..........................................................................................................129 Purchasing Power of a Dollar, Inflation Rate, and Real Income................................132 Stock Index................................................................................................................134 Exercises..................................................................................................................135 SReelvfi-eTewstEExexercricsieses.s...........................................................................................................................................................................................................................113386Chapter 5 140 Mathematics of Merchandising 5.1 Introduction...................................................................................................................1415.2 Trade Discounts..............................................................................................................141 Single Trade Discount ...............................................................................................142 Series of Trade Discounts..........................................................................................144 Single Equivalent Trade Discount Rate for a Series of Trade Discount Rates..........146 Exercises..................................................................................................................1495.3 Payment Terms and Cash Discounts................................................................................152 Payment Terms..........................................................................................................154 Partial Payments........................................................................................................155 Exercises..................................................................................................................1575.4 Markup...........................................................................................................................160 Rate of Markup..........................................................................................................161 Break-Even Price (BE)...............................................................................................164 Exercises..................................................................................................................1655.5 Markdown......................................................................................................................168 Amount of Markdown and Rate of Markdown............................................................169 Exercises..................................................................................................................1725.6 Applications of Markup and Markdown..........................................................................175 Calculating the Reduced Profit or Loss at Sale Price ...............................................175 Exercises..................................................................................................................180

viii Contents PDF Created for Accessibility Purposes Only5.7 Effective Markup and Effective Rate of Markup...............................................................183 Effective Markup .......................................................................................................183 Effective Rate of Markup ..........................................................................................184 Exercises..................................................................................................................187 Review Exercises...............................................................................................................189 Self-Test Exercises.............................................................................................................191Chapter 6 194 Linear Systems 6.1 Introduction...................................................................................................................195 ­Terminology Used in the Rectangular Coordinate System in Graphs........................195 S­ ign Convention........................................................................................................195 Quadrants..................................................................................................................196 Exercises..................................................................................................................1976.2 Graphing Linear Equations.............................................................................................198 Graphing Linear Equations Using a Table of Values..................................................198 Graphing Linear Equations Using the x-intercept and the y-intercept......................199 ­Graphing Linear Equations Using the Slope and the y-intercept...............................199 Exercises..................................................................................................................2056.3 Solving Systems of Linear Equations with Two Variables Graphically...............................206 ­Consistent and Inconsistent Systems........................................................................206 ­Dependent and Independent Equations....................................................................206 Exercises.................................................................................................................2086.4 Solving Systems of Linear Equations with Two Variables Algebraically............................209 The Substitution Method............................................................................................209 The Elimination Method.............................................................................................210 Exercises..................................................................................................................212 SReelvfi-eTewstEExexercricsieses.s...........................................................................................................................................................................................................................221164Chapter 7 218 Break-Even and Cost-Volume-Profit Analysis 7.1 Introduction...................................................................................................................219 Terms used in Break-Even Analysis..........................................................................219 Assumptions and Limitations.....................................................................................221 Break-Even Point.......................................................................................................221 Break-Even Analysis Using a Financial Calculator....................................................222 Exercises..................................................................................................................2237.2 Cost-Volume-Profit (CVP) Analysis...................................................................................225 Exercises..................................................................................................................2307.3 Contribution Margin (CM) Approach to CVP Analysis......................................................232 Exercises..................................................................................................................2357.4 Contribution Margin Ratio..............................................................................................236 Exercises..................................................................................................................2437.5 Graphical Approach to CVP Analysis (Break-Even Chart)..................................................244 Creating and Understanding a Break-Even Chart.....................................................245 Exercises..................................................................................................................249 RSeelvfi-eTewstEExexercricsieses.s...........................................................................................................................................................................................................................225541

PDF Created for Accessibility Purposes Only Contents ixChapter 8 258 Simple Interest and Applications 8.1 Introduction...................................................................................................................2598.2 Calculating Amount of Simple Interest............................................................................259 Notation.....................................................................................................................260 Determining the Time Period in Days Between Dates...............................................262 Exercises..................................................................................................................2668.3 Calculating Principal, Interest Rate, Time, and Maturity Value..........................................268 Calculating the Maturity Value...................................................................................270 Exercises..................................................................................................................2728.4 Calculating Equivalent Payments....................................................................................274 Equivalent Payment of a Single Payment..................................................................275 Equivalent Payment of a Series of Payments............................................................276 Exercises..................................................................................................................2798.5 Applications of Simple Interest.......................................................................................280 Savings Accounts, Term Deposits, and Guaranteed Investment Certificates............280 Demand loans ...........................................................................................................282 Promissory Notes......................................................................................................283 Discounting and Proceeds.........................................................................................285 Treasury Bills and Commercial Papers......................................................................286 Exercises..................................................................................................................288Review Exercises...............................................................................................................290Self-Test Exercises.............................................................................................................292Chapter 9 296 Compound Interest 9.1 Introduction...................................................................................................................297 Notation.....................................................................................................................298 Exercises..................................................................................................................3019.2 Calculating Future Value (FV)..........................................................................................302 Using the Financial Calculator to Solve Problems.....................................................303 Exercises..................................................................................................................3069.3 Calculating Present Value (PV)........................................................................................309 Exercises..................................................................................................................3119.4 Calculating Equivalent Payments....................................................................................313 Exercises..................................................................................................................3179.5 Calculating Periodic Interest Rate (i) and Nominal Interest Rate (j)................................319 Exercises..................................................................................................................3219.6 Calculating Number of Compounding Periods (n) and Time Period (t).............................322 Exercises..................................................................................................................3239.7 Calculating Effective Interest Rate (f)...............................................................................325 Exercises..................................................................................................................3279.8 Calculating Equivalent Interest Rate................................................................................328 Exercises..................................................................................................................330

x Contents PDF Created for Accessibility Purposes Only SRReeelvvfii-eeTewwstEEExxeaxermcricpsileseess.s.........................................................................................................................................................................................................................................................................................................................................333333751Chapter 10 Annuities 34210.1 Introduction...................................................................................................................343 Notation.....................................................................................................................343 Types of Annuities Based on Payment Dates............................................................344 Types of Annuities Based on Compounding Periods.................................................345 Exercises..................................................................................................................34710.2 Future Value and Present Value of an Ordinary Simple Annuity.......................................348 Future Value of an Ordinary Simple Annuity..............................................................348 Using the Financial Calculator to Solve Problems.....................................................350 Present Value of an Ordinary Simple Annuity............................................................353 Exercises..................................................................................................................35710.3 Future Value and Present Value of an Ordinary General Annuity......................................360 Exercises..................................................................................................................36210.4 Future Value and Present Value of a Simple Annuity Due.................................................365 Future Value of a Simple Annuity Due.......................................................................365 Present Value of a Simple Annuity Due.....................................................................366 Exercises..................................................................................................................36910.5 Future Value and Present Value of a General Annuity Due...............................................371 Exercises..................................................................................................................37410.6 Calculating Periodic Payment (PMT)................................................................................377 Exercises..................................................................................................................37910.7 Calculating Number of Payments (n) and Time Period (t).................................................381 Ordinary Annuity........................................................................................................382 Annuity Due...............................................................................................................382 Exercises..................................................................................................................38610.8 Calculating Periodic Interest Rate (i) and Nominal Interest Rate (j)..................................387 Exercises..................................................................................................................389 Review Examples..............................................................................................................391 Review Exercises...............................................................................................................396 Self-Test Exercises.............................................................................................................398Chapter 11 406 Other Types of Annuities 11.1 Deferred Annuities.........................................................................................................407 Ordinary Deferred Annuity.........................................................................................407 Deferred Annuity Due................................................................................................407 Calculating Future Value and Present Value of a Deferred Annuity...........................409 Exercises..................................................................................................................41311.2 Perpetuities ...................................................................................................................415 Exercises..................................................................................................................41911.3 Constant-Growth Annuities ............................................................................................420 Exercises..................................................................................................................424

PDF Created for Accessibility Purposes Only Contents xiSReelvfi-eTewstEExexercricsieses.s...........................................................................................................................................................................................................................442275Chapter 12 430 Amortization of Loans and Mortgages 12.1 Amortization of Loans....................................................................................................431 Amortization Schedule ..............................................................................................431 Constructing an Amortization Schedule ....................................................................432 Calculating the Principal Balance..............................................................................435 Calculating the Final Payment...................................................................................437 Calculating the Interest Portion and Principal Portion of a Payment.........................439 Constructing a Partial Amortization Schedule............................................................442 Exercises..................................................................................................................44412.2 Mortgages......................................................................................................................446 Types of Mortgages ..................................................................................................446 Calculating Mortgage Payments and Principal Balance ...........................................447 Qualifying for a Mortgage..........................................................................................450 Prepaying a Mortgage...............................................................................................450 Exercises..................................................................................................................456Review Exercises...............................................................................................................458Self-Test Exercises.............................................................................................................460Chapter 13Bonds and Sinking Funds 46213.1 Introduction to Bonds.....................................................................................................463 Bond Terminology......................................................................................................46313.2 Calculating Purchase Price and Yield Rate of Bonds.........................................................465 Calculating the Purchase Price..................................................................................465 Calculating the Yield Rate..........................................................................................472 Exercises..................................................................................................................47213.3 Quotation of Bonds ........................................................................................................475 Using the Financial Calculator to Solve Problems.....................................................478 Exercises..................................................................................................................47913.4 Constructing a Bond Schedule........................................................................................480 Amortization of Premium...........................................................................................480 Accumulation of Discount..........................................................................................482 Exercises..................................................................................................................48313.5 Sinking Funds.................................................................................................................484 Sinking Fund Calculations and Constructing a Sinking Fund Schedule....................484 Calculating the Periodic Cost and Constructing a Partial Sinking Fund Schedule....487 Exercises..................................................................................................................489Review Exercises...............................................................................................................491Self-Test Exercises.............................................................................................................493Chapter 14 496Business Investment Decisions 14.1 Introduction...................................................................................................................49714.2 Discounted Cash Flow (DCF)...........................................................................................497 Using the Cash Flow Worksheet to Solve DCF Problems.........................................499 Exercises..................................................................................................................502

xii Contents PDF Created for Accessibility Purposes Only14.3 Net Present Value (NPV)..................................................................................................503 Exercises..................................................................................................................50714.4 Internal Rate of Return (IRR)............................................................................................508 Exercises..................................................................................................................51014.5 Payback Period...............................................................................................................511 Exercises..................................................................................................................513 Review Exercises...............................................................................................................514 Self-Test Exercises.............................................................................................................516Answer key.........................................................................................................518Glossary..............................................................................................................533Index....................................................................................................................537Financial Calculator Instructions....................................................................542Summary of Formulas.......................................................................................544List of Cases, Tables, and ExhibitsCases Applying Percents in Personal Table 3.4 S ummary of Sales Taxes CollectedCase 3 and Business Scenarios.......................... 101 by Canadian Provinces, Applying Ratios in Business.................... 139 Table 4.3(a) as of June 01, 2014.................................93Case 4 Merchandising Cycle of a Product: Currency Cross-Rate Table,Case 5 Manufacturer to Consumer...................... 192 Table 4.3(b) as of January 27, 2014........................... 119 Cost-Volume-Profit Analysis Exchange Rates of Foreign CurrenciesCase 7 at a Manufacturing Company.................. 256 Table 4.4(a) per Canadian Dollar and Vice Versa....... 120 Borrowing and Investing Table 4.4(b) CPI Basket Composition........................ 131Case 8a Using Simple Interest.............................. 293 Table 5.4 CPI from the Year 2002 to 2013.............. 132 Investing in Bank of Canada Table 5.5 Merchandising Calculation Table............. 162Case 8b Treasury Bills.......................................... 294 Table 5.6 Merchandising Calculation Table............. 169 Investing for the Future........................... 338 Table 6.1 Merchandising Calculation Table............. 176Case 9a Borrowing to Start a Business................. 339 Sign Convention of CoordinatesCase 9b Saving for Retirement............................. 400 Table 8.2 in Different Quadrants ........................... 197Case 10a Lease or Finance Option......................... 401 Table to Determine the Number of DaysCase 10b Financial Planning for a Secure Future.... 428 Table 9.1 in a Time Period..................................... 264Case 11 Financing a Growing Business................ 461 Compounding FrequenciesCase 12 Raising Money Through Bonds............... 494 Table 10.1 for Common Compounding Periods........ 299Case 13 Investing in the Stock Market................... 517 Number of Payments per YearCase 14 Table 12.1 for Different Payment Intervals................ 343 Constructing an Amortization Schedule... 432TablesTable 1.1(a) Place Value Chart of Whole Numbers .........3Table 1.1(b) Place Value Chart of Decimal Numbers.......4Table 2.1 Arithmetic Operations and their Meanings................................39Table 2.3(a) Exponents As Repeated Multiplication or Division with Examples........................54Table 2.3(b) Rules of Exponents with Examples...........54Table 2.4 Rules of Logarithms with Examples..........58Table 3.3 Minimum Hourly Wage Rates in Canada, as of June 01, 2014 .................................89

PDF Created for Accessibility Purposes Only xiiiExhibitsExhibit 1.1(a) Place Value of a Ten-Digit Exhibit 7.2(b) When TR = TC, NI is Zero (Break-Even)... 225 Whole Number........................................ 3 Exhibit 7.2(c) When TR < TC, NI is Negative (Loss)...... 226Exhibit 1.1(b) Place Value of a Five-Digit Exhibit 7.3 CM = S - VC...................................... 232 Decimal Number..................................... 4Exhibit 5.3 Sample Invoice with Description of Exhibit 7.5 Graph of Total Costs vs. Quantity Produced Payment Terms.................................... 152 Exhibit 8.1 and Total Revenue vs. Quantity Sold........ 244 Simple Interest�������������������������������������������� 259Exhibit 5.4(a) Relationship Among C, E, P, M, and S..... 161 Exhibit 8.2 Days in Each Month.............................. 262Exhibit 5.4(b) Break-Even Price (BE).......................... 164 Exhibit 8.5(a) Sample Interest-Bearing Promissory Note.284Exhibit 5.5(a) Relationship Among S, D, and SRed.......... 168Exhibit 5.5(b) Relationship Among C, E, P, M, S, D, Exhibit 8.5(b) Sample Non-Interest-Bearing and SRed.............................................. 169 Promissory Note................................... 285Exhibit 5.6 Reduced Profit or Loss After Markdown.... 175 Exhibit 9.1(a) Difference Between Simple Interest and Compound Interest at Different CompoundingExhibit 6.1(a) Rectangular Coordinate System .............. 195 Frequencies......................................... 297 Exhibit 9.1(b) Interest Calculated Upon Interest��������������� 297Exhibit 6.1(b) Ordered Pairs...................................... 196 Exhibit 10.1(a) Types of AnnuitiesExhibit 6.1(c) Quadrants........................................... 196 Based on Payment Dates....................... 344Exhibit 6.1(d) Coordinates in Different Quadrants.......... 196 Exhibit 10.1(b) Types of AnnuitiesExhibit 6.2(a) Graphing a Linear Equation Using Based on Compounding Periods............. 346 a Table of Values.................................. 199 Exhibit 10.2(a) Future Value of OrdinaryExhibit 6.2(b) Graphing a Linear Equation Using the x-intercept and the y-intercept................. 199 Simple Annuity Payments....................... 348Exhibit 6.2(c) Coordinates of Points P and Q................ 200 Exhibit 10.2(b) Present Value ofExhibit 6.2(d) Rise and Run Between Points P and Q..... 200 Ordinary Simple Annuity Payments.......... 354Exhibit 6.2(e) Slope of a Line when ‘m’ is Positive.......... 202 Exhibit 10.4(a) Future Value of Simple Annuity Due Payments ( FVDue )............... 366Exhibit 6.2(f) Slope of a Line when ‘m’ is Negative........ 202 Exhibit 10.4(b) Future Value of OrdinaryExhibit 6.2(g) Slope of a Line Parallel to the X-axis........ 202 Simple Annuity Payments ( FV)............... 366Exhibit 6.2(h) Slope of a Line Parallel to the Y-axis......... 202 Exhibit 10.4(c) Present Value of Simple Annuity Due Payments( PVDue)................ 367Exhibit 6.2(i) Slope of a Line When the y-intercept is 0....203 Exhibit 10.4(d) Present Value of OrdinaryExhibit 6.3(a) Solution of Non-Parallel and Simple Annuity Payments ( PV )............... 367 Intersecting Lines.................................. 207 Exhibit 12.2 Comparison of Principal and Interest Payments of a $300,000 Mortgage at 4%Exhibit 6.3(b) Solution of Parallel and Distinct Lines....... 207 Compounded Semi-annually with Different Monthly Payments�������������������������������������� 451Exhibit 6.3(c) Solution of Parallel and Coincident Lines... 207Exhibit 7.1(a) Graph of Total Costs vs. Quantity �������������� 219 Exhibit 13.1(a) Time-line Diagram Illustrating Bond Payments������������������������������������������� 463Exhibit 7.1(b) Graph of Total Costs vs. Quantity and Total Revenue vs. Quantity������������������������� 220 Exhibit 13.1(b) Inverse Relationship Between Bond Price and Yield Rate�������������������������� 464Exhibit 7.2(a) When TR > TC, NI is Positive (Profit)....... 225 Exhibit 13.3 Comparison of Bonds Selling at Par, Premium, and Discount������������������������������ 475

xiv PDF Created for Accessibility Purposes Only ResourcesTextbook Exercises The textbook has 2000+ Language The language used in this textbook exercises, review exercises, self-test exercises, and comprehensive cases, as well as 300+ is simple and straight-forward, while maintaining solved examples. Problems are designed to test the levels of sophistication required to thoroughly students on real-world, practical applications prepare students for the next stage in their and are presented in increasing levels of academic and professional careers. difficulty, with the most difficult problems being indicated by a dot ( ). The problems Pedagogies and Learning Methods are categorized into pairs of similar questions to provide professors with an opportunity to Numerous pedagogies and learning methods that solve the even-numbered problems in class have been developed and proven over 30 years are and assign the odd-numbered problems as incorporated into the textbook. These pedagogies home work. have succeeded in simplifying critical mathematical concepts and significantly improving retention of Financial Designation Problems The concepts. The different learning methods to solve problems have also proven to cater to the varied textbook contains problems that are used student learning styles. to prepare students for the first level of the Chartered Financial Analyst (CFA) professional Calculator In addition to providing various designation exam. This will provide students with exposure to the financial career choices methods to solve problems, the textbook contains that will be available to them in the instructions to solve problems using the Texas future. These problems are identified by Instruments BAII Plus and Sharp EL-738 financial a ‘CFA Prep.’ icon. calculators, wherever applicable. The calculator instructions are designed using the actual images of the calculator keys, making it easy for students to follow the sequence of operations.Solution Manual All problems in the end-of-section exercises, review exercises, self-test exercises, and cases have been solved using detailed step-by-step methods, including the financial calculator method, as demonstrated in the solved examples. The solution manual is available online.PowerPoint Presentations The animated PowerPoint presentations are available for professors to use in class. They contain both the algebraic and calculator methods of solving problems. The PowerPoint presentations are designed to work with clickers in class to gauge student understanding of concepts.Test Bank A comprehensive test bank, of 3000+ problems in varying levels of difficulty, that covers all concepts in the textbook is provided for professors to use as a database for exercises, quizzes, cases, group projects, or assignments.

PDF Created for Accessibility Purposes Only xvOnline Lessons The online lessons are created as a pre-study component for students. They contain pedagogies that are highly interactive and engaging, and which teach concepts in a very logical and intuitive way. These lessons are not PowerPoint presentations but are interactive movies that have been created to enrich and enhance the learning experience. Every frame is locked to ensure that students go through the lessons sequentially as they are designed to build on learning concepts in succession. The system automatically records students’ progress and performance. Once students complete a lesson, the frame unlocks itself, allowing students to navigate back and forth through the lesson. Professors, on the other hand, have administrative access which allows them to navigate through the online lessons without any restrictions.Online Labs The online lab assessment system contains a rich comprehensive test-bank of real-world problems that are algorithmicallygenerated and that provide students with dynamic feedback on their responses. The labs can also becustomized based on course requirements. A few of the customizable features include, previewingand selecting questions, setting the number of questions, setting and modifying start and due dates,opening, closing and re-opening labs, creating new labs and quizzes, and determining the weightingand number of attempts for each question.Administrative Tools The following administrative tools will provide professors with the ability tomonitor overall class performance and individual student performance on online lessons and labs.Performance Dashboard for Professors Performance Dashboard for StudentsThe lesson performance dashboard provides The lesson performance dashboard providesprofessors with the average completion students with their chapter completion mark,percentage per chapter, including a lesson-by- including a lesson-by-lesson percentagelesson percentage completed visualization for completed visualization. The lab performancethe entire class. The lab performance dashboard dashboard provides them with their labprovides them with the average percentage percentage marks.mark on each lab for the class. Professors canalso download or export individual gradesfor lessons and labs to a spreadsheet or to thecollege’s course management system.Lab Management System The lab management system is provided for administrators or subjectleaders to create new labs, quizzes and case studies, preview and select questions, set the numberof questions, set and modify start and due dates, open, close and re-open labs, and determine theweighting and number of attempts for each question.

xvi PDF Created for Accessibility Purposes OnlyUpdates in the Second EditionThe content of the Second Edition textbook along with its 300+ solved problems, 2000+ exercises, and cases have been carefullyreviewed by professors at various colleges in Canada. In addition to the updates to the texbook, accompanying online resources havealso been updated to reflect the changes.Up-To-DateSection 3.3 Minimum Hourly Wage Rates in Canada, as of June 01, 2014�������������������������������������� 89Section 3.4 Summary of Sales Taxes Collected by Canadian Provinces, as of June 01, 2014�������� 93Section 4.3 Currency Cross-Rate Table, as of January 27, 2014.����������������������������������������������������119Chapters 8 to 14 Interest Rates and Dollar Amounts for Loans and Investments.............................258-519Chapter 12 Mortgage Rates������������������������������������������������������������������������������������������������������������ 446Section 12.2 Prepayment of Mortgages�������������������������������������������������������������������������������������������� 450Modified ContentSection 8.5 Reorganized presentation of Treasury Bills and commercial papers in addition to discounting and proceeds.Chapters 8 to 14 Modified time value of money time-line diagrams for optimal clarity.Chapters 9 to 14 Improved visual format of financial calculator method to show C/Y, wherever applicable.Chapter 11 Improved explanations and derivations for deferred annuities, perpetuities, and constant growth annuities.Section 12.2 Improved explanations for mortgages, qualifying for a mortgage, and prepaying a mortgage.Chapter 13 Improved explanations for bond terminology, quotation of bonds, amortization of premium, and accumulation of discount. Updated method for calculating the purchase price between interest payment dates.New Exhibits and Illustrations Section 3.2 Percent Increase and Decrease������������������������������������������������������������������������������������� 75Section 4.1 Chart on Converting Between Common Units�������������������������������������������������������������� 107Sections 5.4, 5.5, and 5.6 Modified illustrations for markup, markdown, break-even price, and reduced profit or loss���������������������������������������������������������161-175Exhibit 7.1(a) Graph of Total Costs vs. Quantity �������������������������������������������������������������������������������� 219Exhibit 7.1(b) Graph of Total Costs vs. Quantity and Total Revenue vs. Quantity������������������������������ 220Exhibit 8.1 Relationship between simple interest variables������������������������������������������������������������ 261Sections 8.2, 8.3, and 8.5 Time line-diagrams for days between dates, simple interest, and maturity value calculations���������������������������������������������������������������������262-274, 280Exhibit 9.1(a) Difference Between Simple Interest and Compound Interest at Different Compounding Frequencies������������������������������������������������������������������������ 297Section 9.2 Cash-flow sign convention chart��������������������������������������������������������������������������� 303, 351Exhibit 12.2 Comparison of Principal and Interest Payments of a $300,000 Mortgage at 4% Compounded Semi-annually with Different Monthly Payments��������� 451Exhibit 13.1(a) Time-line Diagram Illustrating Bond Payments������������������������������������������������������������� 463Exhibit 13.1(b) Inverse Relationship Between Bond Price and Yield Rate������������������������������������������� 464Exhibit 13.3 Comparison of Bonds Selling at Par, Premium, and Discount������������������������������������� 475

PDF Created for Accessibility Purposes Only xviiNew ContentSection 1.1 Estimation.................................................................................................................................... 9Section 1.4 Addition and Subtraction of Signed Numbers ..........................................................................24Example 1.4(c) Using the Store and Recall Functions to Solve Order of Operation Problems .........................28Section 1.5 Geometric Average (Geometric Mean) .....................................................................................33Example 1.5(h) Finding the Geometric Mean ....................................................................................................33Example 1.5(i) Finding the Average Annual Growth Rate ................................................................................34Examples 3.1(e)-(h) Algebraic Method included: Portion as a Percent of Base ..................................................71-72Section 4.1 Chart on Converting between Common Units ........................................................................ 107Example 4.1(c) Calculating the Hourly Rate of Pay ........................................................................................ 110Example 4.1(d) Calculating the Cost Per Litre.................................................................................................. 110Examples 4.2(a)-(e) Equivalent Ratio Table Method Included ......................................................................... 113-116Examples 4.3(a)-(i) Currency Conversion Table Method Included................................................................... 120-126Section 4.4 Index Numbers and Applications.............................................................................................129Example 4.4(a) Calculating the Index Number and Percent Change in Price of Gasoline in 2014 Using 2002 as the Base Year.....................................................130Example 4.4(b) Calculating the Index Number and Percent Change in the Price of Basic Cable TV in 2014 Using 2002 as the Base Year.....................................130Example 4.4(c) Calculating the CPI and Percent Change in Cost of the Basket of Goods and Services in 2013 Using 2005 as the Base Year....................................131 Calculating the Purchasing Power of a Dollar, Given CPI.......................................................133Example 4.4(d) Calculating the Inflation Rate, Given CPI................................................................................133Example 4.4(e) Calculating the Real Income....................................................................................................134Example 4.4(f) Calculating the S&P/TSX Composite Index.............................................................................134Example 4.4(g) Calculating the List Price, Given the Net Price and a Series of Trade Discount Rates........... 148Example 5.2(j) Calculating the Additional Trade Discount Rate Required.......................................................148Example 5.2(k) Markdown Calculations, Given the Selling Price and Sale Price.............................................169Example 5.5(a) Calculating the Rate of Discount to Match the Competitor’s Sale Price..................................170Example 5.5(c) Calculating the Rate of Markdown to Sell at the Cost Price....................................................171Example 5.5(d) Calculating the Selling Price, Profit or Loss,Example 5.6(c) and Rate of Markdown at Break-Even Price............................................................................177 Calculating the Cost and Rate of Markdown at Sale Price and at Cost Price.........................178 Effective Markup and Effective Rate of Markup ......................................................................183Example 5.6(d) Section 5.7 Effective Markup Calculations, Given the Rate of Markup on Cost and the Rate of Markdown........................................................................183Example 5.7(a) Calculations, Given the Rate of Markup on Selling Price and the Rate of Markdown............. 184 Understanding the Relationship Among Total Cost,Example 5.7(b) Total Sales, and Effective Rate of Markup...............................................................................185Example 5.7(c) Calculating the Effective Rate of Markup on Cost when Items are Sold at Different Prices........................................................186Example 5.7(d) Calculating the Effective Rate of Markup on Selling Price when Items are Sold at Different Prices..............................................................186 Contribution Margin Ratio........................................................................................................236Example 5.7(e) Calculating the Contribution Ratio and Net Income.................................................................238 Calculating the Total Revenue Required toSection 7.4 Break-Even, Given TVC as a Percent of TR...........................................................................238Example 7.4(a) Calculating the Sales Amount and theExample 7.4(b) Contribution Margin Ratio, Given NI, TVC, and FC.................................................................239 Calculating the Additional Sales Required toExample 7.4(c) Break-Even When Variable Costs Increase.............................................................................240 Example 7.4(d)

xviii PDF Created for Accessibility Purposes Only Example 7.4(e) Calculating the Change in Net Income when the Selling Price is Reduced and the Sales Volume is Increased..........................................241 Calculating the Change in Net Income when the Contribution Margin Rate Changes.....242 Example 7.4(f) Creating a Break-Even Chart, Determining Break-Even Revenue Example 7.5(a) and Break-Even Volume, and Computing Break-Even as Percent of Capacity (Maximum Quantity)..........................................................................................................245 Using Break-Even Charts for CVP Analysis......................................................................246 Using Break-Even Charts for CVP Analysis when FC, VC, and S Change......................248 Example 7.5(b) Calculating the Future Value When Principal Balance Declines.......................................305 Example 7.5(c) Calculating the Future Value When Payment Changes....................................................352 Example 9.2(e) Choosing Between Lease and Buy Options and Calculating the Book Value..................373 Example 10.2(c) Calculating the Time Period of a Simple Annuity Due, Given Present Value....................385 Example 10.5(c) Calculating the Present Value of a General Perpetuity Due ............................................417 Example 10.7(d) Calculating the Final Payment of a Simple Annuity Due...................................................439 Example 11.2(b) Example 12.1(f) Calculating the Total Principal Portion and Interest Portion of Payments Made during a Period.........................................................440 Example 12.1(h) Calculating the Principal Reduction and Interest Paid during a Period............................441 Calculating the Effect of an Increase in the Example 12.1(i) Frequency of Payments on the Amortization Period.........................................................454 Example 12.2(e) Calculating the Full Price, Accrued Interest, Quoted Price, and Market Quotation of a Bond................................................................477 Using the Bond Worksheet in a Financial Calculator to Solve Example 13.3(c)...............478 Example 13.3(c) Comparing Two Investment Options Using the DCF Method...........................................499 Example 13.3(d) Example 14.2(c) Acknowledgements The authors and Vretta would like to thank the following professors for their detailed feedback on helping us update the Second Edition of the Mathematics of Business and Finance textbook and its accompanying online resources: ●● Alex Tett, Northern Lakes College ●● Jasmine Birch, Sheridan College ●● Alexei Gokhman, Humber College ●● Jeff Fennell, Fanshawe College ●● Ali Hassanlou, Kwantlen University College ●● Jim Watson, Humber College ●● Amy Goldlist, British Columbia Institute of Technology ●● Karen Jerome, Mohawk College ●● Anish Bania, Douglas College ●● Kit Silcox, Fanshawe College ●● Betty Pratt, Seneca College ●● Leslie Fairbairn, British Columbia Institute of Technology ●● Carol Ann Waite, Sheridan College ●● Mariana Ionescu, George Brown College ●● Colleen Quinn, Seneca College ●● Melanie Christian, St. Lawrence College ●● Deborah Wolff, Sheridan College ●● Mohammad Hussain, Humber College ●● Dianne Krasuski, Humber College ●● Myra Andrews, British Columbia Institute of Technology ●● Edward Clark, Seneca College ●● Nestor Komar, Niagara College ●● Elizabeth Pietrantonio, Mohawk College ●● Rob Smith, Fanshawe College ●● Hardeep Gill, Northern Alberta Institute of Technology ●● Susan Graber, Centennial College ●● Irene Lee, Humber College ●● Teresa Park, Fanshawe College

PDF Created for Accessibility Purposes Only 1 MATHEMATICS OFBUSINESS AND FINANCE Second Edition Larry Daisley, Seneca College Thambyrajah Kugathasan, Seneca College Diane Huysmans, Fanshawe College