A01_HUMM2312_FM.pi-001.indd 2 27/11/13 9:55 PM contemporary business mathematics with canadian applications A01_HUMM2312_FM.pi-001.indd 1 27/11/13 9:55 PM S. A. Hummelbrunner kelly HAllidAy k. SuzAnne coombS contemporary business mathematics with canadian applications 10tH edition Toronto A01_HUMM2312_FM.pi-001.indd 3 27/11/13 9:55 PM Acquisitions Editor: Megan Farrell Marketing Manager: Claire Varley Developmental Editor: Johanna Schlaepfer Program Manager: Patricia Ciardullo Project Manager: Jessica Hellen Production Services: Katie Ostler, Cenveo® Publisher Services Media Editor: Charlotte Morrison-Reed Media Producer: Kelli Cadet Permissions Project Manager: Joanne Tang Photo Permissions Research: Q2a/Bill Smith/Cordes Hoffman Text Permissions Research: Jill Dougan, Electronic Publishing Services Inc. 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HF5691.H85 2014 650.01’513 C2013-904776-X ISBN 978-0-13-305231-2 A01_HUMM2312_FM.pi-001.indd 4 27/11/13 9:55 PM 1.2 fractions v brief contentS Preface … xi Student’s Reference Guide to Rounding and Special Notations … xx Part 1 Mathematics Fundamentals and Business Applications … 2 1 Review of Arithmetic … 4 2 Review of Basic Algebra … 38 3 Ratio, Proportion, and Percent … 84 4 Linear Systems … 133 Part 2 Mathematics of Business and Management … 169 5 Cost-Volume-Profit Analysis and Break-Even … 171 6 Trade Discounts, Cash Discounts, Markup, and Markdown … 201 7 Simple Interest … 246 8 Simple Interest Applications … 277 Part 3 Mathematics of Finance and Investment … 309 9 Compound Interest—Future Value and Present Value … 312 10 Compound Interest— Further Topics … 363 11 Ordinary Simple Annuities … 391 12 Ordinary General Annuities … 432 13 Annuities Due, Deferred Annuities, and Perpetuities … 463 14 Amortization of Loans, Including Residential Mortgages … 517 15 Bond Valuation and Sinking Funds … 569 16 Investment Decision Applications … 613 Appendix I: Further Review of Basic Algebra … 648 Appendix II: I nstructions and Tips for Three Preprogrammed Financia Calculator Models … 668 Answers to Odd-Numbered Problems, Review Exercises, and Self-Tests … 685 Index … 699 A01_HUMM2312_FM.pi-001.indd 5 27/11/13 9:55 PM contentS Preface … xi Student’s Reference Guide to Rounding and Special Notations … xx Part 1 Mathematics Fundamentals and Business Applications … 2 1 Review of Arithmetic … 4 1.1 Basics of Arithmetic … 5 1.2 Fractions … 6 1.3 Applications—Averages … 12 1.4 Applications—Payroll … 18 1.5 Applications—Taxes … 25 BUSINESS MATH NEw S BOX … 29 Review Exercise … 31 Self-Test … 33 Challenge Problems … 34 Case Study Businesses and the GST/HST … 34 Glossary … 36 2 Review of Basic Algebra … 38 2.1 Simplification of Algebraic Expressions …39 2.2 Integral Exponents … 45 2.3 Fractional Exponents … 52 2.4 Logarithms—Basic Aspects … 56 BUSINESS MATH NEwS BOX … 62 2.5 Solving Basic Equations … 63 2.6 Solving Equations Involving Algebraic Simplification …67 2.7 Solving word Problems … 72 Review Exercise … 77 Self-Test … 78 Challenge Problems … 80 Case Study Investing in a Tax-Free Savings Account … 80 Summary of Formulas … 81 Glossary … 82 3 Ratio, Proportion, and Percent … 84 3.1 Ratios … 85 3.2 Proportions … 90 3.3 Percent … 95 3.4 The Basic Percentage Problem … 99 3.5 Problems Involving Increase or Decrease … 106 3.6 Problems Involving Percent … 111 BUSINESS MATH NEwS BOX … 115 3.7 Applications—Currency Conversions … 117 3.8 Applications—Index Numbers … 121 A01_HUMM2312_FM.pi-001.indd 6 27/11/13 9:56 PM contEnts vii 3.9 Applications—Personal Income Taxes … 124 Review Exercise … 127 Self-Test … 129 Challenge Problems … 130 Case Study The Business of Taxes … 131 Summary of Formulas … 132 Glossary … 132 4 Linear Systems … 133 4.1 Algebraic Solution of Systems of Linear Equations in Two Variables … 134 4.2 Graphing Linear Equations … 139 4.3 Graphing Linear Systems of Equations in Two Unknowns … 152 BUSINESS MATH NEw S BOX … 155 4.4 Problem Solving … 156 Review Exercise … 161 Self-Test … 162 Challenge Problems … 162 Case Study Finding the Right Combination … 163 Summary of Formulas … 163 Glossary … 164 Part 1 Comprehensive Case … 165 Part 2 Mathematics of Business and Management … 169 5 Cost-Volume-Profit Analysis and Break-Even … 171 5.1 Cost-Volume-Profit Analysis and Break-Even Charts … 172 5.2 Contribution Margin and Contribution Rate … 187 5.3 Effects of Changes to Cost-Volume-Profit … 191 BUSINESS MATH NEw S BOX … 194 Review Exercise … 196 Self-Test … 197 Challenge Problems … 198 Case Study Segway Tours … 198 Summary of Formulas … 199 Glossary … 200 6 Trade Discounts, Cash Discounts, Markup, and Markdown … 201 6.1 Determining Cost with Trade Discounts … 203 6.2 Payment Terms and Cash Discounts … 211 6.3 Markup … 219 6.4 Markdown … 227 6.5 Integrated Problems … 232 BUSINESS MATH NEwS BOX … 239 Review Exercise … 240 Self-Test … 242 Challenge Problems … 243 Case Study Focusing on Prices … 243 Summary of Formulas … 244 Glossary … 245 A01_HUMM2312_FM.pi-001.indd 7 27/11/13 9:56 PM viii contEnts 7 Simple Interest … 246 7.1 Finding the Amount of Simple Interest … 247 7.2 Finding the Principal, Rate, or Time … 251 7.3 Computing Future Value (Maturity Value)… 256 7.4 Finding the Principal (Present Value) … 258 BUSINESS MATH NEwS BOX … 261 7.5 Computing Equivalent Values … 261 Review Exercise … 273 Self-Test … 274 Challenge Problems … 274 Case Study Cost of Financing Pay Now or Pay Later … 275 Summary of Formulas … 276 Glossary … 276 8 Simple Interest Applications … 277 8.1 Promissory Notes … 278 8.2 Treasury Bills—Present Value … 285 8.3 Demand Loans … 287 8.4 Lines of Credit and Credit Card Loans … 291 8.5 Loan Repayment Schedules … 296 BUSINESS MATH NEwS BOX … 300 Review Exercise … 301 Self-Test … 302 Challenge Problems … 303 Case Study Debt Consolidation … 303 Summary of Formulas … 304 Glossary … 305 Part 2 Comprehensive Case … 306 Part 3 Mathematics of Finance and Investment … 309 9 Compound Interest—Future Value and Present Value … 312 9.1 Basic Concepts and Calculations … 313 9.2 Using the Future Value Formula of a Compound Amount FV = PV (1 + i)n … 319 9.3 Present Value and Compound Discount … 331 9.4 Application—Discounting Negotiable Financial Instruments at Compound Interest … 336 BUSINESS MATH NEwS BOX … 342 9.5 Equivalent Values … 343 Review Exercise … 358 Self-Test … 359 Challenge Problems … 360 Case Study Planning Ahead … 361 Summary of Formulas … 362 Glossary … 362 10 Compound Interest—Further Topics … 363 10.1 Finding n and Related Problems … 364 10.2 Finding i and Related Problems … 372 A01_HUMM2312_FM.pi-001.indd 8 27/11/13 9:56 PM contEnts ix 10.3 Effective and Equivalent Interest Rates … 377 BUSINESS MATH NEwS BOX … 385 Review Exercise … 387 Self-Test … 388 Challenge Problems … 388 Case Study Comparing Car Loans … 389 Summary of Formulas … 389 Glossary … 390 11 Ordinary Simple Annuities … 391 11.1 Introduction to Annuities … 392 11.2 Ordinary Simple Annuity—Finding Future Value FV … 394 11.3 Ordinary Simple Annuity—Finding Present Value PV … 404 BUSINESS MATH NEwS BOX … 413 11.4 Ordinary Simple Annuities—Finding the Periodic Payment PMT … 414 11.5 Finding the Term n of an Annuity … 420 11.6 Finding the Periodic Rate of Interest i Using Preprogrammed Financial Calculators … 425 Review Exercise … 427 Self-Test … 428 Challenge Problem … 428 Case Study Getting the Picture … 429 Summary of Formulas … 430 Glossary … 430 12 Ordinary General Annuities … 432 12.1 Ordinary General Annuities—Finding the Future Value FV … 433 12.2 Ordinary General Annuities—Finding the Present Value PV … 441 12.3 Ordinary General Annuities—Finding the Periodic Payment PMT … 444 12.4 Ordinary General Annuities—Finding the Term n… 447 12.5 Ordinary General Annuities—Finding the Periodic Interest Rate i … 450 BUSINESS MATH NEwS BOX … 451 12.6 Constant-Growth Annuities … 453 Review Exercise … 458 Self-Test … 459 Challenge Problem … 460 Case Study Vehicle Cash-Back Incentives … 460 Summary of Formulas … 461 Glossary … 462 13 Annuities Due, Deferred Annuities, and Perpetuities … 463 13.1 Simple Annuities Due … 464 13.2 General Annuities Due … 477 BUSINESS MATH NEwS BOX … 484 13.3 Ordinary Deferred Annuities … 485 13.4 Deferred Annuities Due … 494 13.5 Perpetuities … 502 Review Exercise … 510 Self-Test … 512 Challenge Problems … 513 A01_HUMM2312_FM.pi-001.indd 9 27/11/13 9:56 PM x contEnts Case Study Planning for University … 514 Summary of Formulas … 515 Glossary … 516 14 Amortization of Loans, Including Residential Mortgages … 517 14.1 Amortization Involving Simple Annuities … 518 14.2 Amortization Involving General Annuities … 538 14.3 Finding the Size of the Final Payment … 544 14.4 Residential Mortgages in Canada … 552 BUSINESS MATH NEwS BOX … 559 Review Exercise … 564 Self-Test … 566 Challenge Problems … 567 Case Study Managing a Mortgage … 567 Summary of Formulas … 568 Glossary … 568 15 Bond Valuation and Sinking Funds … 569 15.1 Purchase Price of Bonds … 570 15.2 Purchase Price of a Bond when Market Rate Does not Equal Bond Rate … 571 BUSINESS MATH NEwS BOX … 584 15.3 Bond Schedules … 585 15.4 Finding the Yield Rate … 590 15.5 Sinking Funds … 593 Review Exercise … 607 Self-Test … 609 Challenge Problems … 610 Case Study Raising Capital Though Bonds … 610 Summary of Formulas … 611 Glossary … 612 16 Investment Decision Applications … 613 16.1 Discounted Cash Flow … 614 16.2 Net Present Value … 621 BUSINESS MATH NEwS BOX … 631 16.3 Rate of Return on Investment … 632 Review Exercise … 644 Self-Test … 645 Challenge Problems … 646 Case Study To Lease or Not to Lease? … 646 Summary of Formulas … 647 Glossary … 647 Part 3 Comprehensive Case … 649 Appendix I: Further Review of Basic Algebra … 652 Appendix II: Instructions and Tips for Three Preprogrammed Financial Calculator Models …672 Answers to Odd-Numbered Problems, Review Exercises, and Self-Tests … 685 Index … 699 A01_HUMM2312_FM.pi-001.indd 10 27/11/13 9:56 PM