1.2: How Can I Use The Features Of This Book To My Advantage?
Formula & Symbol Hub
For this section you will need the following:
Symbols Used
 [latex]C/Y=[/latex] Compounds per year, or compounding frequency
 [latex]FV=[/latex] Future value, or maturity value
 [latex]i=[/latex] Periodic interest rate
 [latex]I/Y=[/latex] Nominal interest rate per year
 [latex]n=[/latex] Number of compound periods
 [latex]PV[/latex] Present value, or principal
Formulas Used

Formula 4.2a – Single Discount
[latex]\text{Single Discount: }\text{Net Price}\text{ = }\text{List Price}\times 1(\text{Discount Rate})\;\rightarrow\;N=L\times(1d)[/latex]

Formula 6.1a – Periodic Interest Rate
[latex]i=\frac{\text{Nominal Rate (I/Y)}}{\text{Compounds per Year (C/Y)}}[/latex]

Formula 6.2a – Number of Compound Periods for Single
[latex]n=\text{C/Y}\times\;\text{(Number of Years)}[/latex]
This textbook was written for students like you, designed to address common student needs in mathematics.
I Don’t Know How to Solve a Math Problem
Do you find it difficult to start a math problem? What do you do first? What is the next step? The reason this is challenging for some students is that they have never been shown problemsolving techniques. This textbook will use a step by step approach to solving problems, as illustrated in the example below. Successfully working through a problem involves a careful approach and this model provides a structured problemsolving approach that will aid you not only in mathematics but in any problemsolving situation you may encounter.
Example 1.2.1
When Sandra borrowed [latex]\$7,100[/latex] from Sanchez, she agreed to reimburse him [latex]\$8,615.19[/latex] three years from now including interest compounded quarterly. What interest rate is being charged?
Solution
Step 1: What are we looking for?
Find the nominal quarterly compounded rate of interest ([latex]IY[/latex]).
Step 2: What do we already know from the question?
The present value, future value, term, and compounding are known, as illustrated in the timeline above (Figure 1.2.1).
[latex]\begin{eqnarray*}PV&=&\$7,100\\FV&=&\$8,615.19\\\text{C/Y}\;&=&\;\text{quarterly}\;=\;4\\\text{Term}\;&=&\;3\;\text{years}\end{eqnarray*}[/latex]
Step 3: Make substitutions using the information known above.
Calculate [latex]n[/latex] using Formula 6.2a[latex]n=\text{C/Y}\times\text{Number of Years}[/latex].
[latex]\begin{eqnarray*}n&=&C/Y\times(\text{Number of Years})\\n&=&4\times3\\n&=&12\end{eqnarray*}[/latex]
Using the [latex]n[/latex] value, we substitute it into the Compound Interest for Single Payments Formula. Rearrange and solve for the Periodic Rate value, [latex]i[/latex].
[latex]\begin{eqnarray*}FV&=&PV{(1+i)}^n\\\$8,615.19&=&\$7,100{(1+i)}^{12}\;\\1.213407&=&{(1+i)}^{12}\\1.213407^\frac1{12}&=&1+i\\1.01624996&=&1+i\\i&=&0.01624996\end{eqnarray*}[/latex]
Substitute [latex]i[/latex] value into Formula 6.1a[latex]\begin{align*}i=\frac{\text{I/Y}}{\text{C/Y}}\end{align*}[/latex] and solve for [latex]\text{I/Y}[/latex].
[latex]\begin{eqnarray*}i&=&\frac{\text{I/Y}}{\text{C/Y}}\\0.01624996&=&\frac{I/Y}4\\I/Y&=&0.06499985\;=\;0.065\;\text{or}\;6.5\%\end{eqnarray*}[/latex]
Note that this amount would be compounded quarterly.
n  I/Y*  PV  PMT  FV  P/Y  C/Y 
[latex]12[/latex]  [latex]6.499985[/latex]*  [latex]7,100[/latex]  [latex]0[/latex]  [latex]8,615.19[/latex]  [latex]4[/latex]  [latex]4[/latex] 
_{*Answer provided by calculations above}
Step 4: Provide the information in a worded statement.
Sanchez is charging an interest rate of [latex]6.5\%[/latex] compounded quarterly on the loan to Sandra.
Try It
1) Use the technique from Example 1.2.1 to plan a vacation. Recall that some methods in this model may have multiple steps.
Solution
Step 1: If you are heading out on vacation, the first thing you want to know is where you are going! Otherwise, how would you get there? In mathematics, you need to figure out what variable you are solving for before you can proceed. This step focuses your problem solving on the end goal. Many students mistakenly rush through this step and start punching numbers on a calculator or plugging numbers into formulas without understanding what it is they are doing. Spend plenty of time on this step, because the remaining three steps do not help at all if you solve for the wrong variable!
Step 2: In planning your vacation, once you figure out where you want to go you need to gather information about your destination. There are things you already know, but there are also things that you do not know, so you need a plan to figure these out. This step helps your problem solving in two ways:

 First, you need to assess what information has already been provided to you. You need to assign values to variables. You may need to draw diagrams to understand how all the numbers fit together.
 Second, you create a plan by which you will solve your problem. Your roadmap identifies how you go from Point A (some variable is unknown) to Point B (knowing what the variable is).
Step 3: Once your vacation is planned, all that is left is to go on vacation! In other words, execute your plan. This step involves all of the mechanics and computations of your roadmap that you developed in the previous step.
Step 4: After you return from vacation, you tell everyone about what you just did. In mathematics, this means you must explain solutions in the context of the question asked. If you just calculated [latex]x=\$700[/latex], what exactly does that represent and how should it be interpreted? Calculating a solution without understanding it is not good enough. A further benefit of this last step is that you can detect errors more easily when you have to explain the solution. For example, read this presentation statement: “If an investor puts [latex]\$1,000[/latex] into a savings account that earns [latex]10\%[/latex] interest, I have calculated that after one year the investor has [latex]\$700[/latex] in her savings account.” Did that make sense? If an account is earning interest, the balance should have become bigger, not smaller! Clearly, the solution of [latex]x=\$700[/latex] must be an error!
Once you repeatedly practice these steps and ingrain this practice in your thinking process, you’ll have a structured approach to solving not just math problems but any life problem. As you keep practicing, you’ll find that this becomes a way of thinking. You can never skip one of the steps, but you won’t have to write them all out anymore because you’ll execute some steps with rapidfire thought!
I Can’t Find What I Want When I Need It
When practicing your business math through homework and assignments, you will need to go back to look up various formulas or techniques or to review concepts. The challenge of most textbooks is in finding what you need when you need it buried in the vast pages of the textbook. Browse the table of contents of this book and notice the functional layout. This textbook incorporates a handbook design that aids in finding information. When you need to look something up, you will notice every part of every section in every chapter is designed and laid out using an identical structure.
While not every part is required in every section, the order is always as follows:
HOW TO
Find Resources Inside of a Textbook Chapter
 Concept introduction
 Concept fundamentals and characteristics
 Formula development and explanation
 Steps and procedures required to solve problems
 Important concept elements and technology use
 Common pitfalls and shared tips
 Conceptual understanding questions
 Guided examples
 Homework exercises
 The start of every chapter includes a miniature table of contents allowing you to locate what you need in the chapter without having to flip back to the book’s main table of contents.
 Endofchapter summaries deliver exactly that—each chapter in a nutshell. They contain key concept reviews, key terms, algebraic symbol definitions, formula summaries, and technology discussions on calculator usage. Links to other chapters are also provided as needed. If you need to look something up, this is the place to start!
Are There Any Steps to Help Me Remember?
Students have always asked if they need to follow a logical sequence of steps to solve a problem. The answer, of course, is YES! A section called “HOW TO” helps you with this by providing stepbystep procedures, techniques, and formulas you need to solve the problem.
Can This Book Help Me Understand the Formulas Better?
You can’t avoid formulas—this is math, after all. What helps, though, is to understand what the formulas do and how each component comes together to produce the solution. If you can understand, you do not need to memorize! This book lays formulas out visually, clearly labelling all symbols. In addition, each component is fully explained (see below). You are not required to crossreference paragraphstyle explanations to formulas, as the visual layout makes it all clear. The goal is for you to understand what exactly the formula does and how, so that you understand enough to recognize when solutions make sense or might be wrong.
[latex]\boxed{4.1\text{a}}[/latex] Single Discount
[latex]{\color{red}{N}}\;\text{is the Net Price:}[/latex] The net price is the price of the product after the discount is removed from the list price. It is a dollar amount representing what price remains after you have applied the discount.
[latex]{\color{green}{L}}\;\text{is List Price:}[/latex] The list price is the normal or regular dollar price of the product before any discounts. It is the Manufacturer’s Suggested Retail Price (MSRP – a price for a product that has been published or advertised in some way), or any dollar amount before you remove the discount.
[latex]{\color{blue}{d}}\;\text{is the Discount Rate:}[/latex] The discount rate represents the percentage (in decimal format) of the list price that is deducted.
Additionally, you will not find any of those archaic algebraic symbols in this book. Representative symbols make the algebra easier to remember and understand. Those ancient mathematicians just loved to speak Greek (literally!), but this text speaks modernday English and understands that we have technology here in the twentyfirst century! We’ll use symbols like [latex]N[/latex] for net price, [latex]L[/latex] for list price, [latex]P[/latex] for profit, and [latex]E[/latex] for expenses, letters that actually remind you of the variable they stand for!
Does Anyone Actually Do Any of This in the Real World?
As you read through the guided examples and do your homework, pause to consider how the question applies to you. Does it demonstrate a business application you can use to be a smarter business professional? How can you extend the question to similar situations? This textbook shows you examples from both business and personal situations that you either have already encountered or probably will encounter in the future. (Remember: Math is all around you!)
 Business
Why do business programs require a business math course in the first term or two? How is it relevant to your future? This textbook provides numerous examples of applications in marketing, finance, economics, accounting, and more. Once you complete this textbook, you should see clearly how business mathematics is relevant and important to your chosen future career.
 Personal
You will see companies and products from your everyday life. Realworld situations show you how to put a few extra dollars in your pocket by making smart mathematical choices. What if you could save [latex]\$100[/latex] per month simply by making smarter choices? Over [latex]40[/latex] years at a very conservative rate of interest, that is approximately [latex]\$100,000[/latex] in your pocket. You will also find life lessons. Are you ready to start planning your RRSP? Would you like to know the basics on how to do this? If you are thinking of buying a home, do you know how the numbers work on your mortgage? To learn how to buy a car at the lowest cost, read on!
Are There Any Secrets?
There are never any secrets. However, I will point out some tricks of the trade and commonly made mistakes throughout this book.
Paths To Success
This feature is designed to make you feel like part of the “in” crowd by letting you take advantage of shortcuts or tricks of the trade, such as some easy way to remember a particular technique or formula. It helps you see how some of the math could be made a little simpler or performed in a different way.
Things to Watch Out For
Awareness of common pitfalls and sources of error in mathematics reduces your chances of making a mistake. A reminder also helps when important concepts are about to be used, reused, or combined in a novel way. It gives you a “heads up” when needed.
Is There Any Way to Know That I’m “Getting It”?
Mastering business math requires two key skills:
 Executing the required techniques and calculations
 Understanding and successfully integrating various mathematical concepts. (For example, when a variable changes, can you estimate how this affects the final result?)
The second skill is much harder to acquire than the first. A feature called “Try It” poses scenarios and questions for which no calculations are required. You need to visualize and conceptualize various mathematical theorems. Ultimately, you perform a selftest to see if you are “getting it.”
In Today’s World, Who Does This By Hand Anymore?
That is a perfectly valid question. You are right: Most people do not do this work by hand and instead use mathematical tools such as calculators, spreadsheet software, and apps. However, as the saying goes, you must learn to walk before you can run. The learning of mathematics requires pencil and paper first. Once you master these, you can then employ technology to speed up the process. This basic version textbook incorporates one technology to aid you in your application of business mathematics:
 The Calculator
Integrated throughout this book are instructions for one of the financial calculators most widely used in Canada—the Texas Instruments BAII Plus. Calculator functions with stepbystep button sequences are presented with guided examples illustrating how you solve the math problem not only by hand but also using the financial calculator.
Is There Any Way I Can Assess My Ability?
At the end of almost every section of this book you will find approximately 18 practice questions covering the concepts specifically introduced in that section, with final solutions listed to all questions at the end of this textbook. These questions are divided into three categories to help develop your mathematical skills and assess your abilities:
Mechanics
This group of questions focuses on fundamental mathematical skills and formula usage. They are your first taste of using the section formulas and working with the mathematical concepts at an introductory level.
HOW TO
Be Successful in Business Math Mechanics
Successful completion of these questions means that you:
 Have at least a basic understanding of the variables at play,
 Show rudimentary application of concepts, and
 Can calculate solutions using the formulas.
Do not stop here, though! You do not yet have enough skills to meet the basic requirements of most business math courses. Once you have mastered the Mechanics section, you must progress to the next section, where you learn to apply your knowledge.
Applications
These questions are more typical of business math course expectations (check with your instructor). The key difference from the Mechanics section is that you must now execute your problemsolving skills. These questions require you to determine the unknown variable and figure out how the various pieces of the puzzle come together in the solution.
HOW TO
Be Successful in Business Math Applications
Successful completion of these questions means that you:
 Understand concepts at a satisfactory level,
 Can problem solve typical business math applications, and
 Can successfully integrate concepts at an acceptable performance level.
Challenge, Critical Thinking, and Other Applications
These questions put your knowledge and understanding to the test. The difficulty bar is set high, as these questions commonly require multistep solutions with advanced problemsolving techniques. As well, success might require you to integrate formulas, concepts, or procedures in novel ways. You will be challenged!
HOW TO
Be Successful in Business Math Critical Thinking
Successful completion of these questions means that you:
 Understand concepts at an aboveaverage level,
 Can problem solve in difficult situations, and
 Can successfully integrate concepts at a higher level of thinking.
THE FOLLOWING LATEX CODE IS FOR FORMULA TOOLTIP ACCESSIBILITY. NEITHER THE CODE NOR THIS MESSAGE WILL DISPLAY IN BROWSER.[latex]n=\text{C/Y}\times\text{Number of Years}[/latex][latex]\begin{align*}i=\frac{\text{I/Y}}{\text{C/Y}}\end{align*}[/latex]
Attribution
“Chapter 1: Succeeding in Business Mathematics” from Business Math: A StepbyStep Handbook (2021B) by J. Olivier and Lyryx Learning Inc. through a Creative Commons AttributionNonCommercialShareAlike 4.0 International License unless otherwise noted.