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PrefaceIntroductionContemporary Business Mathematics with Canadian Applications is intended for usein introductory mathematics of finance courses in post-secondary business management, marketing, accounting, and fi ance programs. It also provides a review of basicmathematics.The primary objective of the text is to increase the student’s knowledge and skill inthe solution of practical fi ancial and operational problems encountered in operatinga business.Organization318ChAPTEr 9COMPOUND INTErEST—fUTUrE vALUE AND PrESENT vALUEContemporary Business Mathematics with Canadian Applications is a teaching textusing problem-identifi ation and problem-solving approaches. The systematic andsequential development of the material is illustrated by examples that show a step-bystep approach to solving the problem. The detailed solutions are presented in a visuallyclear and colourful layout that allows learners to monitor their own progress in theclassroom or in independent study.Each topic in each chapter is followed by F. Calculating the numerical value of the compounding factor (1 1 i )practice exercises containing numerous drillquestions and application problems. At the endof each chapter, Review Exercises, Self-Test, and aCase Study integrate the material presented.The fi st four chapters and Appendix I (FurtherReview of Basic Algebra) are intended for studentswith little or no background in algebra and providean opportunity to review arithmetic and algebraicprocesses.The text is based on Canadian practice, and reflects current trends using available technology—specifi ally the availability of preprogrammed fi ancial calculators.Students using this book should have access to calculators having a power functionand a natural logarithm function. The use of such calculators eliminates the constraintsassociated with manually calculating results using formulas.In solving problems involving multiple steps, often values are determined that willbe used in further computations. Such values should not be rounded and all availabledigits should be retained in the calculator. Using the memory functions of the calculator enables the student to retain such non-rounded values.W hen using the memory the student needs to be aware that the number of digitsretained in the registers of the calculator is greater than the number of digits displayed.Depending on whether the memory or the displayed digits are used, slight differencesmay occur.Students are encouraged to use preprogrammed fi ancial calculators. The use ofthese preprogrammed calculators facilitates the solving of most fi ancial problems andis demonstrated extensively in Chapters 9 to 16.(iii)(iv)(v)(vi)(vii)12% p.a. compounded quarterly for 12.5 years;10.5% p.a. compounded monthly for 10.75 years;8% p.a. compounded quarterly for 30 months;9.5% p.a. compounded semi-annually for 42 months;5.8% p.a. compounded daily for 2 years.SOLUTION(1 1 i ) nmn(i)5% 5 0.05114(1) 5 14(1 1 0.05)14 5 1.0514(ii)7% 4 2 5 0.035215(2) 5 30(1 1 0.035)30 5 1.03530i412.5(4) 5 50(1 1 0.03)50 5 1.035010.5% 4 12 5 0.008751210.75(12) 5 129(1 1 0.00875)129 5 1.00875129(v)8% 4 4 5 0.02430/12(4) 5 10(1 1 0.02)10 5 1.0210(vi)9.5% 4 2 5 0.0475242/12(2) 5 7(1 1 0.0475)7 5 1.04757(vii)5.8% 4 365 5 0.000159*(iii)12% 4 4 5 0.03(iv)365(1 1 0.058/365)730 5 (1.000159*)7302(365) 5 730*roundednThe numerical value of the compounding factor, (1 1 i)n, can now be computed usingan electronic calculator. For calculators equipped with the exponential function featurey x , the numerical value of the compounding factor can be computed directly.STEP 1Enter the numerical value of (1 1 i) in the keyboard.STEP 2Press the exponential function key y xSTEP 3Enter the numerical value of n in the keyboard.STEP 4Press 5STEP 5Read the answer in the display. Continue calculating or save as needed.The numerical values of the compounding factors in Example 9.1C are obtained asfollows:(i)(ii)STEP 1Enter1 1 0.05STEP 2PressyxSTEP 3Enter14STEP 4Press5STEP 5read1.9799322.806794(iii)(iv)1 1 0.07/2 1 1 0.12/4 1 1 0.105/12yx(v)(vi)(vii)1 1 0.08/41 1 0.095/21 1 95554.3839063.0766471.218994Note: Do not be concerned if your calculator shows a difference in the last decimal.There is no error. It reflects the precision of the calculator and the number of decimalplaces formatted to show on the display of the calculator.For example, if your calculator has been set to show only two decimal places, it willautomatically round the answer to (i) above to 1.98. If you were to continue calculatingM09 HUMM2312 CH09.p309-362.indd 318A01 HUMM2312 FM.pi-001.indd 1105/09/13 12:06 PM27/11/13 9:56 PM

xiip r e fa c eNew To This EditionThe Tenth Edition of Hummelbrunner/Halliday/Coombs, Contemporary BusinessMathematics with Canadian Applications, includes updates based on changes in current practices in Canadian fi ance and business and the needs of students and instructors using this book. Th s edition continues to clarify the consistent approach to rounding rules. TheStudent’s Reference Guide to Rounding and Special Notation (pages xx–xxiii)gives a clear explanation of the rounding conventions used throughout the text.Additional Pointers and Pitfalls boxes are placed in key areas to remind studentsabout the rounding conventions and exceptions in practice. The text and solutions manual have been thoroughly technically checked for accuracy and consistency with the rounding approach. Tables, charts, and further diagrams have been added to enable the learner to visualize the problems and the solutions. Numerous new examples and exercises have been added. Chapter 5 has been signifi antly revised with emphasis on the relationships betweenparts of CVP. Break-even charts are integrated with theory by introducing them afterexplanations of revenue and cost behaviour. Chapter 6 has been signifi antly revised with standardized formulas and wording,illustrated by visual approaches to solving the problems. Canadian references have been emphasized in Business Math News Boxes and websitereferences. Interest rates refl ct current investment and borrowing rates.Many examples and exercises have been updated, rewritten, and expanded. To enhancethe building-block approach, exercises are ordered to link the topics and the solvedexamples. Help references have been expanded to link selected exercises to solvedexamples.Specifi ally, in Chapter 1 (Review of Arithmetic), prices, salaries, and wages havebeen updated. Revised rates and calculations for GST/PST/HST have been included toincorporate new legislation for 2012 and property tax terminology and valuations havebeen updated.In Chapter 2 (Review of Algebra), the chapter-opening vignette emphasizes whybusiness students need algebra, and new exercises have been added to utilize formulasfor simple and compound interest. Calculator solutions have been introduced for several examples and formulas have been simplifi d.In Chapter 3 (Ratio, Proportion, and Percent), a consistent approach for calculating proportions has been introduced, and formulas throughout the chapter have beenupdated for consistency. Drill questions have been replaced by more word problems,and alternative solutions have been included. Currency conversion rates, prices, CPInumbers, and personal income taxes have been updated.In Chapter 4 (Linear Systems), the comparison/substitution method for solvingthe point of intersection of two linear systems has been emphasized. A new BusinessMath News Box ties more closely to the chapter-opening vignette and introduces amanufacturing capacity example.The order of Chapter 5 and Chapter 6 has been switched in the Tenth Edition toimprove the fl w of content from Linear Systems (Chapter 4) to Cost-Volume-ProfitAnalysis and Break-Even (Chapter 5). Th s chapter has been changed signifi antly,beginning with an updated title to refl ct break-even as an application of the profitfunction, not the focus of the chapter. The opening vignette now includes an example that connects with the Business Math News Box presented later in the chapter. TheA01 HUMM2312 FM.pi-001.indd 1202/12/13 8:03 PM

p r e fa c exiiinumber of formulas has been reduced, and solutions to examples use a simplifi dapproach for calculating break-even.Chapter 6 (Trade Discounts, Cash Discounts, Markup, and Markdown) haschanged signifi antly. For consistency and clarity, terminology and explanationshave been simplifi d and formulas have been standardized. New Pointers andPitfalls boxes provide tools to help students rearrange formulas, determine thenumber of days in a discount period, and calculate markup. A sample invoicedemonstrates payment terms and cash discounts. EOG and ROG examples thatappeared in the Eighth Edition of the text have been added back in this edition.In Chapter 7 (Simple Interest), the chapter-opening vignette ties in with thechapter’s Business Math News Box. Dates and interest rates have been updated andnew exercises have been added, with exercises referenced to examples. Additionalcomments for choosing focal dates have been added, with a section included showing an example of the use of Excel functions.In Chapter 8 (Simple Interest Applications), the use of grace periodshas been updated, with exercises omitting its use. Comments on credit ratings,credit scores, home equity lines of credit, and new exercises using credit cards havebeen added. Treasury bill interest rates have been updated to refl ct current rates.A new Business Math News Box addresses the question, “How do you learn aboutmoney?”In Chapter 9 (Compound Interest—Future Value and Present Value), visualexplanations have been expanded. The introduction to Future Value, and explanation of the periodic rate of interest, have been simplifi d. The relationship betweenn and m has been clarifi d, with a new formula added to explain the calculation ofn. The calculation of a partial year to a rounded number has been eliminated, keeping the year as a fraction. A new section showing Excel’s FV and PV calculationsis included, with visual examples. New figures have been added. The number ofreview and self-test exercises has been reduced to eliminate duplication. Formulashave been simplifi d with the elimination of references to S and P.In Chapter 10 (Compound Interest—Further Topics), formula variations havebeen identifi d, explained, and illustrated. A Pointers and Pitfalls box has beenadded to address formula rearrangement. Several examples have been rearrangedto show the simpler examples fi st. New sections have been added to illustrate theuse of Excel functions. New exercises and new charts are included. The issue ofdebt repayment is addressed in a new Business Math News Box.In Chapter 11 (Ordinary Simple Annuities) and in Chapter 12 (OrdinaryGeneral Annuities), new business application exercises and examples with diagrams have been included. New Pointers and Pitfalls boxes have been added toremind students about clearing calculator inputs, using inversion techniques whencalculating, understanding the term “payment,” and the calculator’s positive/negative sign convention. The explanation regarding the purpose of method for presentvalue calculations has been expanded. A new Business Math News Box refers to apopular and successful Canadian entrepreneur.In Chapter 13 (Annuities Due, Deferred Annuities, and Perpetuities), explanations, diagrams, and calculations for annuities due are simplifi d. The order ofsome examples has been changed to provide a more logical and intuitive learningsequence. New examples with diagrams have been added, including reference toinvestments in preferred shares. A new Pointers and Pitfalls box reminds the readerhow to calculate periodic interest rates on the calculator.In Chapter 14 (Amortization of Loans, Including Residential Mortgages), anew section with a diagram develops the skills to fi d the interest, principal, andA01 HUMM2312 FM.pi-001.indd 1327/11/13 9:56 PM

xivp r e fa c ebalance for a period, and bridges between fi ding the payment and constructing theamortization schedule. The introduction to residential mortgages has been updated torefl ct current legislation on mortgage insurance. Examples and exercises have beenreordered and clarifi d to enhance building-block learning.In Chapter 15 (Bond Valuation and Sinking Funds), explanation of basic conceptshas been expanded to answer the “why?” questions. The order has been changed, with afocus on calculation of bond price under different conditions. An introductory sectionhas been added for concept comprehension. Calculating the purchase price of a bondhas been separated into two sections based on whether or not the market rate equals ordoes not equal the bond rate. A new Business Math News Box describes and discussesCanada Savings Bonds.In Chapter 16 (Investment Decision Applications), explanations begin the section on Net Present Value, followed by introductory, then more advanced, applications.Repetitive calculator instructions have been eliminated. Computing the Rate of Returnby manual methods has been condensed and new visuals have been added.Comprehensive Case StudiesComprehensive case studies for each part of the book have been created. The questions within each case study have been separated by chapter or group of chapters tofacilitate the use of these case studies by those institutions that include only some of thetopics in their course syllabus. W ith the questions separated and identifi d by chapter,these institutions can use part of the case study in their courses.Part 1 Mathematics Fundamentals and Business ApplicationsTil Debt Do Us Part host Gail Vaz-Oxlade has made it her mission to help couples whoare headed for disaster get out of debt. Questions for each of Chapters 1–4 are included.Part 2 Mathematics of Business and ManagementA sporting equipment manufacturer and retailer, SportZ Ltd., is based in Alberta.Questions for each of Chapters 5–8 are included.Part 3 Mathematics of Finance and InvestmentBased in Ontario, Lux Resources Group, Inc., rents and sells construction equipment.Questions for each of Chapters 9–16 are included.In general, interest rates used refl ct the current economic climate in Canada.Calculator tips and solutions have been updated or clarifi d. Spreadsheet instructionsand Internet website references have been updated. Pitfalls and Pointers have beenincluded to assist in performing tasks and interpreting word problems, and sectionshave been rewritten to clarify the explanations. Many more word problems have beenadded and references to solved examples have been added. Business Math News Boxesand Case Studies have been updated. Examples involving both business and personalsituations are included. The pedagogical elements of the previous edition have beenretained. In response to requests and suggestions by users of the book, a number ofnew features for this edition have been included. They are described below.FeaturesUpdated! A new colourful and student-friendly design has been created for the book, makingit more accessible and less intimidating to learners at all levels.322CHAPTER 9COMPOUND INTEREST—FUTURE VALUE AND PRESENT VALUEtable 9.3 Financial Calculator Function Keys That Correspond to Variables Used in Compound Interest CalculationsUpdated! Any preprogrammed fi ancial calculator may beused, but this edition includes extensive instructions for using the Texas Instruments BA II PLUSfinancial calculator. Equivalent instructionsFunction KeyalgebraicSymbolVariableThe number of compounding periods1tiBa ii pluSSharpEl-738CNnnHp10bii1Ni1/YRThe periodic annuity payment2PMTPMTPMTPMTThe present value or principalPVPVPVPVThe future value or maturity valueFVFVFVFVThe rate of interestNotes:iI/YC/Y1. The periodic rate of interest, (i ) is entered as a percent and not as a decimal equivalent (as it is whenusing the algebraic method to solve compound interest problems). For example, 8% is entered as “8”not “.08.” With some calculators, the rate of interest is the periodic rate. In the case of the BA IIPlus, the rate of interest entered is the nominal rate per year I/Y .2. The periodic annuity payment function key PMT is used only for annuity calculations, which areintroduced in Chapter 11.Using the Texas Instruments BA II PlUs to solve Compound Interest ProblemsFollow the steps below to compute the future value of a sum of money using the formula FV PV(1 i)n and a Texas Instruments BA II Plu S calculator. Compare yourresult with that in Example 9.2A.pre-calculation phase (initial Setup)sTEP 1A01 HUMM2312 FM.pi-001.indd 14The P/Y register, and behind it, the C/Y register, must be set to match the calculator’sperformance to the text presentation. The P/Y register is used to represent the numberof regular payments per year. If the text of the question does not discuss regular payments per year, this should be set to equal the C/Y in the calculator. The C/Y registeris used to represent the number of compounding periods per year; that is, the com-27/11/13 9:56 PM

xvp r e fa c eare given in Appendix II for the Sharp EL-738Cand the Hewlett-Packard 10bII financialcalculators.new! Each part opens with an introduction to theupcoming chapters and a discussion of therounding conventions that are relevant to thesechapters.10.1ChapTer The Pointers and Pitfalls boxes emphasizegood practices, highlight ways to avoid common errors, show how to use a fi ancial calculator effici tly, or give hints for tackling businessmath situations to reduce math anxiety.Upon completing this chapter, you will be able to do the following:❶ determine the number of conversion periods and find equateddates.❷ Compute periodic and nominal rates of interest.❸ Compute effective and equivalent rates of interest.»Discount 5 5% of 560 5 0.05 3 560 5 28.bUsiness math news bOxnational salary ComparisonsKnowing how much you are worth in the job market is critical for not being underpaid. Successful salary negotiations are accomplished by having accurate information. In today’s electronic age, the Internet offers a variety of websites focusing on05/09/13salary information.Th ee popular job functions along with the respective salaries are listed belowby major metropolitan location.M10 HUMM2312 CH10.p363-390.indd 363Financial ControllerResponsible for directing an organization’s accounting functions. These functions include establishing andmaintaining the organization’s accounting principles, practices, and procedures. Prepares financial reportsand presents fi dings and recommendations to top management.Human Resources ManagerPlans, directs, and coordinates the human resource management activities of an organization to maximizethe strategic use of human resources and maintain functions such as employee compensation, recruitment,personnel policies, and regulatory compliance

Contemporary Business Mathematics with Canadian Applications is intended for use in introductory mathematics of finance courses in post-secondary business manage-ment, marketing, accounting, and fi ance programs. It also provides a review of basic mathematics. The primary objective of the