Mathematics of Finance and Commerce
Pure and Applied Mathematics 20
 
Top | Overview | Materials | Activities | Assessment | Outcomes | Student Instructions | Review | Salaries and Wages | Property Tax | Exchange Rates | Unit Pricing | Keeping Track of Money | Loans and Investments | Sample Project | Progress Report | end
Overview
Introducing all students to the mathematics of finance and commerce has been called for by many groups over the years. Clearly, this is one of the areas that people in our society feel is important for all students. In the past, students may or may not have been exposed to some, or all of the topics in these areas depending on the choices their teachers made with respect to teaching number concepts, nunber operations and problem solving. In the new program, outcomes related to the mathematics of finance and commerce are made explicit for all students by specifying them as common outcomes in the pure and applied programs.
The following is a sameple of a unit of self-study unit for Mathematics 20. Given that the outcomes in this unit require a limited number or prerequisite skills, this may be the unit that students can work on independently of group instruction hence freeing up class time for concepts that require more explicit and intense instruction.
The mathematics of finance and commerce unit could be assigned to students at the very beginning of the year. To complete the unit, students must be able to set up ratios involving percents, compute percents, solve linear equations, solve equations involving exponents, and construct tables and graphs with and without the use of technology. Activities are built in to the unit to guide students through these processes.
Alternatively, teachers could use these materials as a guide for their teaching.
 
Materials
MathPower 11 or Addison-Wesley Mathematics 11 textbook
Graphing Calculator
Internet
Spreadsheet software
Handout: Mathematics of Finance and Commerce Unit
 
Activities
Review Unit
See student unit
Students complete unit of self-study over a period of _______ weeks.
Students monitor their own progress with a chart which is handed in to the teacher.
Students request assistance when faced with difficulties.
Teachers distributes quizzes at the student's request.
Teacher marks quizzes and projects
Teacher assigns supplementary work in areas the student needs assistance
Create projects and assessment items
 
Assessment
For this unit the students are to keep track of their work and their progress on the "self-directed learning progress report" (see back of unit). Teachers are responsible for monitoring that the students are doing this and for assessing the student's need for further work in the concepts and skills that are to be learnt in this unit. Each student should demonstrate what they have learnt either in an assignment or a set of quizzes.
One of the ways that teachers might want to think about assignments (that is, the tasks the students will hand in to demonstrate their learning) is the time demand placed on the students. A crude way of classifying such tasks is:

short: These tasks might be word problems which are solved with a known formula or process and take most students just a few minutes (e.g. How much interest will Chuck earn if he deposits $350 for 2.5 years if the interest of 1.75% is compounded annually? or Which is a better buy, a 550 g box of cereal for $2.50 of a 1 kg box of cereal for $5.00?
medium: This may be an investigation that takes an hour or two. In this case, the student would have relevant information at hand but the problem would require the student to do things like test cases, develop a proof, or explicate a line of reasoning. (e.g. Using the information given and a spreadsheet compare leasing a car and buying one, or using your own financial situation, prepare a monthly budget, using the information given, reconcile this cheque book with the bank statement.)
long: This may be an extended project that would involve the collection of material and finding information from a variety of sources. For a single unit a student may have to do a number of short problems, a couple of medium ones, and possibly a long project. The teacher may consider giving the student a choice of which sections to pull each type of assignment from. (Assume you want to take a trip (buy a car, stereo etc.) one year after you complete school. Investigate the cost and prepare a budget shows how you could be in the financial position to do so. Compare the cost of borrowing money to purchase a car and leasing a car (no information given). Which would you choose to do? Explain your reasoning).

It may be useful to think of having the students complete a couple of short problems for each section, one medium investigation for each section and one project for the whole
unit. The students would be able to select from a variety of tasks.
 
Outcomes
Note that these are common outcomes to both Mathematics 20 and Applied Mathematics 20
General Outcome:
Solve consumer problems, using arithmetic operations.
Specific and Process Outcomes:
C4-1 Solve consumer problems, including: wages earned in various situations; property taxation; exchange rates; unit prices. Connections, Estimation, Problem Solving, Reasoning and Technology
C4-2 Reconcile financial statements including: cheque books with bank statements; cash register tallies with daily receipts. Connections, Problem Solving, and Technology
C4-3 Solve budget problems, using graphs and tables to communicate solutions. Communication, Problem Solving, Technology, and Visualization
C4-4 Plot and describe data of exponential form, using appropriate scales. Communication, Technology, and Visualization
C4-5 Solve investment and credit problems involving simple and compound interest. Connections, Problem Solving, and Technology


Self-Study Unit for Mathematics 20

Overview
The material in this booklet is intended for self-study and is to be used in conjunction with the MathPower 11 or Addison-Wesley Mathematics 11 textbook. The unit contains links to the Internet for further application of each concept and additional resources that will be of benefit to you. Access to the Internet and TI-83 calculator will be an asset when completing this unit.
This is an alternative form of learning that allows you to work at your own pace. You are responsible for the assignments and work in this unit and for completing the assessment requirements at the end of each section.
You will have the most success with this unit if you read the instructions very carefully so that you know what is expected of you.
Outcomes
By the end of this unit you are expected to:
Solve consumer problems, including: wages earned in various situations; property taxation; exchange rates; unit prices. This includes making connections, estimating, problem solving, reasoning and using technology
Reconcile financial statements including: cheque books with bank statements; cash register tallies with daily receipts. This includes making connections, problem solving, and using technology.
Solve budget problems, using graphs and tables to communicate solutions. This includes communicating with mathematics and about mathematics, visualizing graphs and using technology.
Plot and describe data of exponential form, using appropriate scales. This includes communicating with mathematics and about mathematics, visualizing graphs and using technology.
Solve investment and credit problems involving simple and compound interest. This includes making connections, problem solving and using technology.
Instructions to students
1. Complete the pretest.
If you have difficulty with some items on the pretest you must consult with your teacher to work on your prerequisite skills.
2. Read the explanations and consider the examples in unit and textbook.
3. Complete the exercises and problems assigned.
4. Record the work you have completed on the form "self-directed learning record".
5. When you have finished the unit, turn self-directed learning record into teacher and ask for final assignment and/or test.
6. Complete and turn in assignment/project/quiz to teacher.
Note If you have difficulty with a particular type of question and/or problem, there are a number of things you can do:
go back to the appropriate section in the text;
ask a friend for help;
ask your teacher for help.
Check your skills
Understand and do computations with common fractions, decimal fractions, percent and money.
Percent
Recall that a percent is a number out of 100 (i.e. 68% = 68/100).
Consider the following examples.
Find 68% of $12 645.
Set-up a ratio.
68 = x__
100 12645
Multiply both sides by 12 645.
68(12 645) = x
100
Calculate
x = 8598.60
Hence, 68% of $12 645 is $8598.60.
 
What percent is $4.55 out of $65.00?
Set up a ratio.
4.55 = x__
65.00 100
Multiply both sides by 100.
4.55 (100) = x
65.00
Calculate.
x = 7
Hence, $4.55 out of $65 is 7%.
 
Recall that a percent can be expressed as decimal and a decimal as a percent.
Convert 12% to a decimal.
12 = x
100
x = 0.12
 
Convert 0.075 to a percent.
0.075 = x_
100
0.075 (100) = x
x = 7.5%
 
Check your skills
1) Calculate 75% of $16 348
2) 20% of an amount is $1.60. What is the original amount?
3) $120.00 is what percent of $4000.00?
4) Convert 7.9% to a decimal.
5) Convert 0.78 to a percent.
6) Convert 0.0015 to a percent.
7) Convert 4/5 to a percent.
8) Convert 15/20 to a decimal.
9) Multiply 150 by .25
10) Multiply 1200 by .05
 
 
Section 1: Salaries and Wages

Earning Money
This section will deal with the different ways that people get their paycheck! Most likely, if you have had a job, you have been paid on an hourly basis or possibly by the piece (delivering papers for example). This are only two of the ways that people get paid. There are 4 main ways of determining one's pay for work.
Reading Exercise
MathPower 11 Section 9.1 Earning Income
Read and work over examples on pages 527 - 530.
Addison-Wesley Mathematics 11 Section 1.5 Earning a Living
Read and work over examples pages 37 - 40
Before you complete the exercises for this section, show you know the similarities and the differences among them by writing definitions for the following terms.
Hourly Rate (Wage)
Salary
Piecework
Commission
Gratuities
Exercises
MathPower 11 Section 9.1 Earning Income
Do questions pages 530 - 531:
Addison-Wesley Mathematics 11 Section 1.5 Earning a Living
Do questions pages 40 41: 1, 5, 6, 7, 8, 9, 11, 12
Deductions
If you have had a job, you may have noticed that you made a certain amount, but you never actually got that amount of money on your cheque! That's because of deductions like Canadian Income Tax (CIT), Employment Insurance (EI), and Canada Pension Plan (CPP). The amount of money you make before these deductions is called your gross income and the money you actually get to put in the bank is called your net income or net earnings.
Reading Exercise
MathPower 11 Section 9.2 Net Income
Read pages 532 - 535. Work through the examples.
Mathematics 11 Section 1.6 Taking Home a Pay Cheque
Read pages 45-47. Work through the examples and then consider the questions posed in Discussing the Ideas on page 48.
Before you complete the exercises for this section, explain the purpose of each of these deductions and how they are computed.
Canada Pension Plan (CPP)
Employment Insurance (EI)
Income Tax
Provincial Tax
Write definitions for the following terms.
Gross Income
Net Income
Exercises
MathPower 11 Section 9.2 Net Income
Pages 536-537, questions 1-4, 5 - 7, 13 - 16, 18 - 20, 22, 24, 26, 27 - 28, 33 - 35
Mathematics 11 Section 1.6 Taking Home a Pay Cheque
Pages 48-50, questions 3, 4, 5, 7, 9, 10, 11, 13, 14. Write a response to communicating the ideas at the bottom of page 50.

Section 2: Property Taxes

Every home or building is assessed for a property tax. What this means is that the government will charge a tax to the owner for being on land that is a part of the province or country. The government will determine what to charge the owner by assessing different aspects about the property.
Fair Market Value: This is how much the property is worth, taking into consideration age and the value when it was first built.
Assessed Value: This is a percent of the fair market value of the property.
Mill Rate: This is a tax rate that the government will set. This is determined locally.
One Mill = (1/1000) of $1
Property Tax: A person's or company's property tax rate is assessed by using the formula:
Reading Exercise
MathPower 11 Section 9.6 Housing Costs
Read bottom of page 558 and page 559. Consider example 2.
Mathematics 11 Section 1.7 Determining Expenses
Read page 53 and consider example 2.
To learn more about the nature of property taxes browse around the "Canadian Property Tax Association" website at:
http://www.cpta.org
 
Exercise
MathPower 11 Section 9.6 Housing Costs
Page 560, questions 14 - 16, 20 - 22, 29, 30, 31, 32, 36
Mathematics 11 Section 1.7 Determining Expenses
Page 55, questions 5, 6, 12 and questions below.
1. The residential mill rate for a town is 34.0725. Calculate the annual property tax for assessed values of:
a) $ 89 000 b) $125 500 c) $325 900
2. The mill rate for business (commercial) property is 45.0009. Calculate the annual property taxes for the following assessments:
a) $550 000 b) $2 400 000 c) $12 500 000
Section 3: Exchange Rates

Before beginning this section, you need to understand how exchange rates are used. If you have access to the Internet, go to
http://www.rubicon.com/passport/currency/currence.html
or
http://www.currency.co.nz

and look for the currency exchange. You can input an amount of money from any country and it will give the amount it would be worth in every other country using the exchange rate of each country!

Investigate: Find out what an exchange rate is and how it works. Why do different countries have different exchange rates? How are they determined?
Each country has their own determined exchange rate. It is defined as:
"the ratio at which a unit of the currency if one country can be exchanged for that of another country; also called rate if exchange" (Excite Reference, 1999)
If you have traveled before, you know that one Canadian dollar is worth something different in the United States or in Ireland. This is because each country sets their own economy and these rates reflect their economical situations. Do you know what the Canadian Dollar is worth in US Dollars right now? Go back to the website noted above and find out.
example: How much is $50 Canadian dollars worth in U. S. dollars?
Reading Exercise
MathPower 11
Turn to page 526 and look at the chart given there reflecting the exchange rates of each country compared to Canada. What do these numbers represent?
Mathematics 11 Section 1.7 Determining Expenses
Read page 52 and consider example 1. What does each number in the example represent? How was the currency converted?
Exercise
MathPower 11 Investigating Math: Foreign Exchange
Page 526, questions 1 - 7.
Mathematics 11 Section 1.7 Determining Expenses
Page 55 - 56, questions 7 - 11.
 
Section 4: Unit Pricing

Unit Prices ­ Have you ever gone grocery shopping and seen two boxes of the same laundry detergent, but in different sizes? Which is the better buy? Would it be better if you buy the bigger one even though you don't really need all of it?
 
To understand unit pricing better, go to:

http://www.fmi.org/consumer/unit
This will give a brief description of unit pricing and how it works! At the top of the page, there will be four boxes. After you have read the first page, go to "Using Unit Pricing". After you have read this page, go to "More Information". Then try out your new knowledge by clicking on the box "Test Yourself".
Unit pricing is a tactic companies and supermarkets sometimes use to influence shoppers. For example, you may go to a local convenience store and see the sign:

2 Chocolate Bars for $1.29
(89 cents each)

It would be less expensive for each one if you buy two, but do you really want two? How much is each bar if you buy two at the special price? Is this a better deal?
Exercises
MathPower 11 Getting Started
Page 524, questions 1 - 4.
Mathematics 11
Page 54, questions 1 , 2.
 
Section 5: Keeping Track of Money

Budgeting
If you have ever had a job or even an allowance, you know that when you spend that money, you will eventually run out! That's why you have to "budget" this money so that you have paid for all the things that are the most important. A balanced budget is one in which the total expenditures (spending) equals the total income.
Reading Exercise
MathPower 11 Balancing a Budget
Read pages 562 - 564 and work through examples offered.
Mathematics 11 Section 1.8 Preparing a Budget
Read pages 61 - 65 and work through the examples offered.
Many financial Institutions (banks for example) have web pages that will help you prepare a budget. Here are two sites interesting sites. (You need to download a large file from the Royal bank site to use their budget planner.)

http://www.tdbank.ca/student/stbud.html
http://www.Royalbank.com/student

Assignment
MathPower 11 Balancing a Budget
Pages 565 - 566, questions 1 - 10. 15 - 17, 19, 21 - 25 and 28
Mathematics 11 Section 1.8 Preparing a Budget
Pages 66 - 68, questions 1 - 8 and questions below.
1. Use pie chart question 3 page 66 and assign a category for each of the following expenses.
a) bus pass b) shampoo c) a video rental d) bike repairs
2. Determine whether each of the following represents a deficit or a surplus.
  Total Income Total Expenditures
a) 1250.00

1180.00
b) 36 500.00 38 200.00
c) 27 750.00  27 750.00
 
Keeping Track of Money
One of the services a bank offers when you put your money into one of their chequing accounts is a bank statement. Each month the bank sends the customer a record of the account transactions. These include deposits, cash machine withdrawals, cheques written on the account, service charges and deposits.
When a person compares the bank statement to their own personal record of transactions they reconcile their records.

Retail stores, too, do reconciliations. They balance cash register tallies with daily receipts at the end of every business day. Taking what you know about reconciling a personal bank account, what do you think reconciling a store's sales involves?
Reading Assignment
MathPower 11 Financial Statements
Pages 567-569
Mathematics 11 Keeping Track of Your Money
Pages 58 - 60
Exercises
MathPower 11 Financial Statements
Pages 569, questions 1- 3, and 1, 2 (bottom of page).
Mathematics 11 Keeping Track of Your Money
Pages 58 - 60, questions 1 - 6.
 
Section 6: Loans and Investments

When you take out a loan from a bank, they will charge you interest on the money that you borrow. Conversely, if you deposit money in the bank, like you do when you buy a GIC or Canada Savings Bond or put your money in a savings account, you make interest on the money you lend them!
Simple Interest
If the interest is made on the loan annually, we call this simple interest. Simple interest is sometimes also called regular interest.
Reading Assignment
MathPower 11 Section 9.3 Interest and Annuities
Read page 538 and do the Inquire questions 1 - 4.
Mathematics 11 Section 1.1 Savings and Credit: Simple Interest
Read pages 4 - 8 and work examples.

Exercises
MathPower 11 Section 9.3 Interest and Annuities
Page 538, questions 1 - 4.
Mathematics 11 Section 1.1 Savings and Credit: Simple Interest
Pages 9 - 11, questions 3, 6, 7, 8, 10, 13, 15, 16.
Compound Interest
Compound interest differs from simple interest in that the interest made in one interest period will be left in the bank and will itself earn interest in the next period.
Reading Assignment
MathPower 11 Section 9.3 Interest and Annuities
Read pages 540 - 542 and work through the examples.
Mathematics 11 Section 1.2 Compound Interest
Read pages 14-16 and work through examples 1-4.
Mathematics 11 Section 1.3 Compounding Periods Less than One Year
Read page 21 - 23 and work through examples.

Exercises
MathPower 11 Section 9.3 Interest and Annuities
Page 542, questions 13 - 35.
Mathematics 11 Section 1.2 Compound Interest, Section 1.3 Compounding Periods Less than One Year
Pages 17 - 19, questions 1, 3, 5, 10, 12, 15, 20.
Pages 24 - 27, questions 3, 4, 5, 7, 9, 10, 12, 13, 15, 19, 22

Time Value of Money: Using the Graphing Calculator (TI-83)
The TI-83 calculator has what is called the TVM which stands for the "Time Value of Money"

Exercises
MathPower 11 Financial Calculations using a Graphing Calculator
Read pages 544-545 and do questions 1 - 4 and 1 - 5.
Mathematics 11 Investigating Financial Calculations on the TI-83
Read pages 28-29 and do questions 1 - 5.

Investment and Credit
Reading Exercise
MathPower 11 Section 9.5 Consumer Credit
Read pages 551 - 555 and work through examples
MathPower 11 Section 9.6 Housing Costs
Read pages 557 - 559 and work through examples
Mathematics 11 Section 1.4 Comparing Financial Options
Read pages 30 - 34 and work through examples
Mathematics 11 Section 1.9 Investigating Mortgages
Read pages 69 - 71 and work through examples

Common Banking Applications
After working through "Section 6 Loans and Investments" you should be able to describe each of the following. Write your own explanation for each term. If you need further information about any of these terms, use the Internet to go to a financial institutions home page. Information about all of these things is readily available.
Term Deposit
Guaranteed Investment Certificate (GIC)
Registered Retirement Savings Plan (RRSP)
Mortgage
Amortization
Credit Cards
Credit Rating
Reading Exercise
MathPower 11 Section 9.5 Consumer Credit
Pages 555 - 556, questions 1, 3, 5, 11, 12, 16, 17, 21, 22, 26, 28, 30, 31
MathPower 11 Section 9.6 Housing Costs
Pages 560 - 561 questions 1, 2, 5, 6, 9, 10, 26, 27, 28, 38
Mathematics 11 Section 1.4 Comparing Financial Options
Pages 32 - 33: Investigate - Selevting the Best Borrowing Scheme Questions 1 - 4
Mathematics 11 Section 1.9 Investigating Mortgages
Pages 71 - 74 questions 1, 2, 3, 5, 6, 7, 9, 11, 12
Sample Project

Mathematics of Finance and Commerce

The following is a sample of a project assessment. This can be given to the student who fully completes this unit as a final assessment. This should be offered as an alternative to a unit exam.
 
Your First Home
You decided to buy your first home, and you are wondering how much you can afford. Imagine you are paid a gross salary of $45 000 a year. Calculate your monthly paycheck if you are only subject to the three main deductions each month (EI, CPP and CIT)
Look through the paper and find a house that you like. It must be at a price that you think you can afford with your monthly paycheck. You need to go to the bank and see how much each monthly mortgage payment will be. The bank tells you they will give you a mortgage amortized over 15 years at an interest rate of 7% fixed for the entire term.
Plan a brief budget, including mortgage payments, utilities, cable, insurance, property taxes, car payment, food, recreation, and miscellaneous. Calculate your property taxes with a mill rate of 18.375. The assessed rate will be the price you purchased the house at. Calculate your car payment as if it were $400 including insurance and miscellaneous items. You should show evidence that you have actually researched these costs and they are realistic!
Your income should be more than your expenses, or your house costs too much! Make sure you stay within your boundaries!
Good Luck!
 
This project will be marked on the following standards:
10 marks ­ monthly paycheck with correct deductions
20 marks ­ correct mortgage and property tax calculations
10 marks ­ balanced budget with realistic and researched expenses
Total Marks: 40 marks
 
Self-Directed Learning Progress Report
 
 
   Student Comments  Teacher Comments
 Pretest    
 Section 1    
 Section 2    
 Section 3    
 Section 4    
 Section 5    
 Section 6    
 Student-Self evaluation  I planned my time and spread the work out  Yes No
 I read the readings carefully  Yes No
 I worked the examples  Yes No
 I completed all the assigned questions  Yes No
I kept good records of my learning  Yes No
 Comments

 What did you learn about yourself doing this independently?

What should the teacher know about your experience with this self-study?

 

 

 



 
 
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