MathPFinance.doc

The Tower of Babel

Summative Activity and Assessment Plan

Professor: Jamie Pyper

Students : Jonathan BlanksonIhsan Rehman

Mihaela TingireSection 003

Table of Contents

Overview.............................................................................................................................................3Background Information.....................................................................................................................3Teacher Instructions............................................................................................................................4Day #: 1 Topic: Canada Savings Bond..........................................................................................5Day #: 2 Topic: The Budget Sheet...............................................................................................6Day #: 3 Topic: The Cost of Credit..............................................................................................7Worksheet 1........................................................................................................................................8Worksheet 2........................................................................................................................................9Game Worksheet..............................................................................................................................10Worksheet 3......................................................................................................................................11Solutions: Worksheet 1.....................................................................................................................12Solutions: Worksheet 2.....................................................................................................................14Game Sheet Solutions.......................................................................................................................15Solutions: Work Sheet 3...................................................................................................................17

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Overview

This summative activity is for the grade 11 College preparation, Mathematics of Personal Finance, MBF3C. This course enables students to broaden their understanding by investigating income opportunities, interest analysis, mathematics of financial growth, sequences and series and their financial applications, mathematical calculations related to finance of real world projects like transportation, accommodation, automobiles and managing their money, career choices and a summative unit on planning the student’s financial future.

At a point in time of our lives we are left to make decisions which affect us for the rest of our lives and college level students are no exception. They have to make informed decisions on whether or not they are going to run their own business, rent or buy a house, lease or buy a car, etc. Therefore, each student will use the mathematics presented in this course throughout their lifetime. This summative assignment covers "Exponential Functions", "Financial Applications" involving "Simple and Compound Interests" and "Annuities". The main objectives of our summative activity refer to the students' abilities to :

Make informed decisions about "Canada Savings Bond"

Solve problems involving simple and compound interests and annuities

Solve and making decisions on problems involving leasing or buying properties

Prepare a budget sheet for a small company

Background Information

"A small city, Babel, which was struggling economically decided to take the world by storm by building a very big and tall tower (which they aimed to make it more attractive than the famous Tower of Paris) to attract tourists and travelers alike to the city in order to boost their economy. A committee was set to make this wonderful dream come through. After first meeting the committee approached a Scotia Bank to let them know what they were doing so that as soon as they finished their estimate they could get a loan from them. But the Scotia Bank asked them to raise funds and invest in the Canada Savings Bond to get some capital before they could lend them the rest of the money needed for the project and they have to submit their budget to show that the project would be profitable."

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Teacher Instructions

This summative unit is broken into three days as it follows :

Day Activity K/U TIPS CO APP

1 Canada Savings Bonds 4 - 5 10

2 The Budget Sheet/Game 5 - 9 25

3 The Cost of Credits - - 5 20

All the teaching and learning strategies are outlined in the daily lesson plans

Student worksheet handouts are featured for each of the three days

The assessment strategies (marking schemes and rubrics) as well as the solutions for each activity are provided under the Solutions section of this document.

Note: The Game Sheet is part of Day #2. Students should be given the background information below. The amortization tables are part of the solutions; in order to receive full marks the students should implement and submit them using spreadsheet software (e.g. MS Excel)

Background Information

A small city, Babel, which was struggling economically decided to take the world by storm by building a very big and tall tower (which they aimed to make it more attractive than the famous Tower of Paris) to attract tourists and travelers alike to the city in order to boost their economy. A committee was set to make this wonderful dream come through. After first meeting the committee approached a Scotia Bank to let them know what they were doing so that as soon as they finished their estimate they could get a loan from them. But the Scotia Bank asked them to raise funds and invest in the Canada Savings Bond to get some capital before they could lend them the rest of the money needed for the project and they have to submit their budget to show that the project would be profitable.

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LESSON PLAN MBF3C Mathematics of Personal Finance

Day #: 1 Topic: Canada Savings Bond

REVIEWSimple interest and compound interest

HANDOUTS / TECHNOLOGY Worksheet 1: Canada Saving Bond Activity Computers connected to the internet

TEACHING EXPECTATIONSStudents will :

Know and distinguish between various Canada Savings Bond types Solve problems involving the simple interest formula (I=Prt) Solve problems involving the calculation of the amount (A) and the principal (P) in

the compound interest formula A = P(1+i)n

CURRICULUM REFERENCESThe Ontario Curriculum Grades 11 and 12 Science, 2000 pg. 29

LESSON OVERVIEWThis activity should be done in a computer lab or classroom with computers connected to the Internet. Students can work independently or in a group of two or more depending on the number of computers available. A brief review of formulae involving the simple interest and compound-interest would be advantageous for the students. As well, students may be allowed to quietly converse in pairs on the problems as they require total understanding to correctly use the given formulas. The teacher should make sure that all students have logged on to Canada Savings Bond web site following the link given on the worksheet. The teacher should be available throughout this work period to clarify any problems the students might have.

METHOD OF ASSESSMENTThis period will be formally evaluated as part of the total assignment mark. The assessment includes a marking scheme : Knowledge - 4 marks, Application -10 marks, Communication - 5 marks and a rubric based on four levels for the evaluation of the thinking and communication skills.

ENRICHMENT Question 3 can be modify using

different interest rates Draw a graph to compare the

accumulated interest earned after each year for the two types of regular or compound interest bonds

REMEDIATION Give students extra time if they require

or they can complete the work at home and submit it the next day

Guide students to organize the chart

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Day #: 2 Topic: The Budget Sheet

REVIEWThe concepts of present value and regular payment in the formula for the present value of an ordinary annuity.

HANDOUTS / TECHNOLOGY Worksheet 2: The Budget Sheet Activity Game Sheet Computers with spreadsheet software or

TI-83 Plus calculators

TEACHING EXPECTATIONSStudents will :

Design a budget suitable for a small company Explain and justify budgets, using appropriate mathematical forms Compare the cost involved in buying or leasing the same vehicle or office


LESSON OVERVIEWThis activity can be done in a computer lab or classroom with computers (with spreadsheet software) or TI-83 Plus calculators can be used. Students can work independently or in groups of two or more, depending on the number of computers or TI-83 Plus calculators available. A brief review of formulae that are important for the calculation of the regular payment and the present value in the formula for the present value of an ordinary annuity would be helpful for the students. As well, students may be allowed to quietly converse in pairs on the problems as they require total understanding to correctly use the formulas given. The teacher should be available throughout this work period to clarify any problems the students might have. For the game part (i.e., if the students finish early) the teacher should divide students into four home groups. Two people in each home group are going to become experts on one question on the game sheet. The two experts for, say question #1, from each home group move to the same table to solve question #1. The same for question #2 and so on. After mastering their topic, the two experts for each question move to their home group to share their solution in turns with the rest of their group. Each home group submits one solution and all group members receive the same mark.

METHOD OF ASSESSMENTThe teacher will formally assess the students, using a marking scheme: Knowledge - 5 marks, Application - 25 marks, Communication - 9 marks and a rubric based on four levels for the evaluation of the thinking and communication skills.

ENRICHMENT Have students to research to come out

with the cost of building a tower bigger than that of Paris

More problems can be added to the game sheet

REMEDIATION Give students extra time if they required Guide students to come out with good

and reasonable expenses relative to the company in question

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Day #: 3 Topic: The Cost of Credit

REVIEWThe present value and the regular payment in the formula for the present value of an ordinary annuity

HANDOUTS / TECHNOLOGY Worksheet 3: The Cost of Credit Activity Computers with spreadsheet software or TI-83 Plus calculators

TEACHING EXPECTATIONSStudents will:

Solve problems involving the calculation of the present value and the regular payment in the formula for the present value of an ordinary annuity

Build an amortization table for repayment schedule to calculate the total interest paid on loans

Know and make decisions on good loan deals


LESSON OVERVIEWThis activity can be done in a computer lab or classroom with computers (with spreadsheet software) or TI-83 Plus calculators can be used. Students can work independently or in groups of two or more depending on the number of computers or TI-83 Plus calculators available. A brief review of formulae that are important for the calculation of the present value and the regular payment in the formula for the present value of an ordinary annuity would be helpful for the students. As well, students may be allowed to quietly converse in pairs on the problems as they require total understanding to correctly use the given formulas. The teacher should be available throughout this work period to clarify any problems the students might have.

METHOD OF ASSESSMENTThis period will be formally evaluated as part of the total assignment mark, using the following marking scheme: Application - 20 marks and Communication - 5 marks.

ENRICHMENT Have students solve problems

involving different interest rates and deals

REMEDIATION Give students extra time if they require Guide students to make the repayment

schedule

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Worksheet 1

Canada Savings Bond Activity MBF 3CName: Due Date:

Information is found at the following link: www.csb.gc.ca/eng/ then go to Bonds and Rates then go to Canada Savings Bonds or Canada Premium Bonds. Many Questions can be answered at FAQ

1. What are Canada Savings Bonds? CO [ /2]

2. For each of the two main product types of Canada Savings Bonds, generate a chart that includes the following heading: CO and TIPS (the rubric is provided in the Solutions section )

a) Bond Types

b) Types of interest options available for Canada Savings Bonds

c) Current Rates for each bond type

d) Redeemable Period

e) Who is eligible to own Canada Savings Bonds?

f) Where you can purchase the Bonds?

g) Range of the values of Bonds purchases.

3. The rate of a CSB (Canada Savings Bonds) is 3.90% and for CPB (Canada Premium Bond) is 4.70%. Suppose the Tower of Babel committee were able to raise some funds and decided to invest $ 50, 000 in each of the four types of bonds available and will be redeemed at maturity in 5 years.

a) Determine the total interest they will earn for each investment APP [ /10]

b) Determine the difference in the total interest earned for the regular interest CSBs and the regular interest CPBs K/U [ /2]

c) Determine the difference in the total interest earned for the compound interest CSBs and the compound interest CPBs K/U[ /2]

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http://www.csb.gc.ca/eng/

d) Explain why the differences in parts b) and c) are not the same CO [ /3]

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Worksheet 2

The Budget Sheet Activity MBF 3CName: Due Date:

The Tower of Babel committee needs money to build the tower, to buy or to lease company’s cars, to rent or to buy offices, etc. After considering all these factors they saw that they needed $2,000,000 besides the initial capital they raised and put in the Canada Savings Bonds. But before they can get a loan from the bank, they are required to submit their monthly budget report to the bank, so that the bank could

evaluate the business 's credibility (based on the monthly profit).

Based on the committee’s research, they estimated that on the average the company is going to receive 20,000 visitors in a month and they plan to charge $5 per visitor. Assuming this is the only source of income for the company;

1. Calculate the total revenue of the company K/U [ /2]

2. Prepare a monthly budget sheet for the company. Note: use the sample Monthly Budget Worksheet on page 364 of your textbook as a guide (you may use the spreadsheet to prepare the budget sheet for convenience) CO and TIPS

3. Calculate the total expenses of the company K/U [ /3]

4. Determine the difference between the total revenue and the total expenses. This is the net income for the company APP [ /5]

5. Based on your budget sheet explain whether the company is going to be profitable or not. CO [ /5]

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Game Worksheet

1. Demonstrate, through calculation, the advantages of early deposits to long-term

savings plans (e.g., compare the results of making an annual deposit of $1000 to an RRSP, beginning at age 20, with the results of making an annual deposit

of $3000, beginning at age 50) APP[ /5]

2.

Ali is going to buy or lease a new car which cost $25000. To lease, he has to pay 550 per month for 5 years. To buy, he has to finance the car at an interest rate of 2%, compounded monthly over 5 years.

a) Find the monthly payment required. PP [ /5]b) Determine whether he should buy or lease CO [ /2]

3. Mary and John have rented a 2 bedroom apartment for 5 years. They are paying the rent and the utilities. Since they are expecting their first child, they are considering buying a house. They saved $3,000 last year and $2,500 the year before, for their down payment.

Apartment Costs House Costs Rent: $1,150/month Gas: $900/year Electricity: $550/year Apt Parking: $30/month

Mortgage: $260/week Electricity: $230/month Water: $55/month Property Taxes: $1980 / year

Should they buy the house? Justify your answer. App [ /5] and CO [ /2]

4. Jill needs $1,200 two years from now. How much should she deposit at the end of

each quarter for next two years in an account that pays 4% compounded interest quarterly. APP [ /5]

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Worksheet 3

The Cost of Credit Activity MBF 3CName: Due Date:

After the Tower of Babel committee submitted their budget, the Scotia Bank saw that the project was going to be great and more importantly, all things being equal, the project would make a lot of profits.

The Scotia Bank offered to give the project committee a loan of $ 2,000,000 for 5 years at a rate of 6% compounded monthly. But the TD Canada Trust Bank heard about the deal and decided to give the project committee a 2% cash back of the loan as soon as they sign up for the loan. Also, their deal includes a loan of $2,000,000 for 6 years at a rate of 7.5% compounded monthly.

Using the information given about the two banks above:

a) Calculate the monthly payment of the Scotia Bank deal APP [ /3]

b) Calculate the monthly payment of the TD Canada Trust deal. APP [ /3]

Use the monthly payment for each deal respectively to do the following:

c) Build an amortization table for the repayment schedule for the Scotia Bank deal using a spreadsheet or a TI – 83 Plus calculator APP [ /5]

d) Build an amortization table for the repayment schedule for the TD Canada Trust Bank deal using a spreadsheet or a TI – 83 Plus calculator APP [ /5]

e) Calculate the total interest paid on the loan for each deal APP [ /4]

f) Write a short note to advice the project committee the best deal to consider CO [ /5]

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Solutions: Worksheet 1

1. Canada saving bond is a financial product issued by the Bank of Canada. It offers a competitive rate of interest and guarantees a minimum interest rate .Now these bonds include two product types:

The Canada Savings Bond (CSB) The Canada Premium Bond (CPB) CO [ /2]

2. Bond Types The Canada Savings Bond

(CSB) The Canada Premium Bond

(CPB)

Interest Options Regular Interest Compound Interest

Regular Interest Compound Interest

Current Rate Year 1 - 2.0% Year 1 - 2.5% Year 2 - 3.25% Year 3 - 4.0%

Redeemable Period Any time Only on the anniversary of the issue date and for 30 days thereafter

Eligibility The CSB may be owned by Canadian residents. Federal and provincial government employees, including armed forces personnel and their immediate family, stationed outside the country may also purchase the CSB.

The CPB may be owned by Canadian residents. Federal and provincial government employees, including armed forces personnel and their immediate family, stationed outside the country may also purchase the CPB.

Where you can Purchase

Can be purchased online for ease and convenience. The CSB can also be bought wherever you bank or invest, or by calling 1 888 773-9999. The CSB can also be purchased through payroll deduction where available at sponsoring employers.

Can be purchased online for ease and convenience. The CPB can also be bought wherever you bank or invest, or by calling 1 888 773-9999.

Range of Values You can buy a CSB for as little as $100 – or for as little as $2 per week on the Payroll Savings Program. The maximum amount you can generally own per series is $500,000 per type of registration (for exceptions, please refer to the terms and conditions).

You may buy a CPB for as little as $100. The maximum amount you can generally own per series is $500,000 per type of registration (for exceptions, please refer to the terms and conditions).

See the rubric below for the assessment of the communication and thinking skills.

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Rubric for Worksheet 1Level 1 Level 2 Level 3 Level 4

Communication

Chart uses little of the correct data and is poorly organized

Chart uses some of the correct data and is satisfactorily organized

Chart uses many of the correct data and is organized good

Chart uses all of the correct data and is well organized

Thinking/Inquiry

Summary and rationale unclearPoorly written

Difficult to follow or interpret .Few spelling or grammar errors.Adequate presentation of information

Useful info; good format.Well written.Some variety in presentation of information.

Well presented; strong reflection of ministry expectations High quality composition.Enhanced presentation of information.

3. (a) Given the principal, P = $ 50,000, and the time, t = 5 years

For CSB we have the rate, r = 3.90% APP [ /5] To calculate the regular interest, use the formula,

I = (50,000)(0.039)(5) I = $ 9,750 therefore, the regular interest for the CSB is $ 9750

To calculate the compound interest rate, use the formula, P = 50,000, t = 5, i = 3.9% A = 50,000(1 + 0.039)5

A = $ 60,540.742 using a calculator .So, interest, I is I = A - P I = 10540.742 - 50000 I = $10540.74 therefore, the compound interest for the CSB is $ 10540.74

For CPB we have the rate, r = 4.70% APP [ /5] To calculate the regular interest, use the formula,

I = (50000)(0.047)(5) I = $11,750 therefore, the regular interest for the CPB is $ 11750

To calculate the compound interest rate, use the formula, P = 50,000, t = 5, i = 4.7% A = 50,000(1 + 0.047)5

A = $62,907.643 using calculator So, interest, I is

I = A - P I = 62,907.643- 50,000 I = $ 12907.64 therefore, the compound interest for the CPB is $ 12907.64

3. (b) The difference in the total interest earned for the regular interest CSBs and the regular interest CPBs is $ 11750 - $ 9750 = $ 2000 K/U [ /2]3. (c) The difference in the total interest earned for the compound interest CSBs and the compound interest CPBs is $ 12907.64 - $10540.74 = $ 2366.90 K/U [ /2]3. (d) The difference in parts (b) and (c) are not the same because for regular interest the interest is calculated only once on the principal amount whereas, for compound interest the interest is calculated on both the principal amount and the interest earned. CO [ /3]

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Solutions: Worksheet 2

1. The total revenue of the company is: K/U [ /2] (number of visitors) x (ticket price) = 20,000.00 x 5 = $ 100,000.00

2. The monthly budget sheet may look like the one below but not exactly the same.

Monthly Budget Sheet

Rubric for Worksheet 2, Part 2 - assessment of Communication and TIPS

Level 1 Level 2 Level 3 Level 4Communicatio

nBudget sheet is poorly organized with poor use of assumptions

Budget sheet is satisfactorily organized with adequate use of assumptions

Budget sheet is well organized with good use of assumptions

Budget sheet is excellently organized with excellent use of assumptions

Thinking/Inquiry

Rationale unclearAnd poorly related to the budget in question.

Difficult to follow or interpret .Few spelling or grammar errors.Adequate presentation of budget in question.

Useful info; good format.Well written.Some variety in presentation of budget in question.

Well presented; strong reflection of budget in question. High quality composition.Enhanced presentation of budget in question.

RevenueNumber of visitors 20000 Ticket Price $ 5.00 Total Revenue $ 100,000.00

ExpensesElectricity $ 400.00 Gas $ 300.00 Office Supplies $ 200.00 Property Tax $ 1,500.00 Cleaning Staff $ 8,000.00 Secretarial $ 2,200.00 Managers $ 16,500.00 Advertisement $ 12,000.00 Repairs Cars $ 300.00 Insurance $ 350.00 Repairs $ 300.00 Equipment Repairs $ 1,500.00 Postage $ 150.00 Rent $ 3,087.00 Equipment $ 4,000.00 Gas Cars $ 550.00 TotalExpenses $ 51,337.00

Net Income 48,663.00

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3. The total expenses of the company is $ 51,337.00 (note: this should base on how they prepare the budget sheet). K/U [ /3]

4. The net income of the company is: (total revenue) - (total expenses) = 100,000.00 - 51,337.00 APP [ /5] = $ 48,663.005. Based on the results in the worksheet we can conclude that the company will be profitable, with a net income of $ 48,663.00 monthly. CO [ /5]

Game Sheet Solutions

1. Lets assume that the annual interest rate is 8%, the retirement age is 60 years, the saving process starts at age 20 years with an annual deposit of $1,000. Then we have a regular deposit R=1,000, an interest rate i=0.008 and a number of deposits n=40. APP [ /5]

the amount,

= 1,000 .

= 25,9056.519A $ 25,9056.52

Also, for the deposit of $3,000 annually at age 50 we have R=3000, i=0.08, n=10.

the amount ,

= 43,459.687A $43,459.69

Therefore, from the calculations we can see that the early deposit is more advantageous than the long-term savings plan.

2. (a) The car's present value, V=$25,000.00 APP [ /5]

Monthly interest rate

Number of deposit The monthly payment is calculated using the formula :

= 438.192R

the monthly payment is $438.19.

(b) He should buy because the monthly payment $438.19 > $450 and also he is going to own the car as his property. CO [ /2]

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3. APP [ /5]Apartment Cost/year House Costs/year

Rent $1150 x 12=13,800.00Gas $900.00Electricity $550.00Apt. Parking $30.00 x 12=$ 360.00

Mortgage $260.00 x 52=$13,520.00Electricity $230.00 x 12=$2,760.00Water $55.00 x 12=$660.00Property Taxes $1,980.00

Total $15,610.00 Total $18,920.00

They should buy the house because the difference between the costs (monthly/yearly) of the two options is not too much. Also, when they buy the house, it will be their own property , which they can sell at a later date CO [ /2]

4) Given the amount, A=$1,200.00, APP [ /5]the number of quarterly deposit, n=4 x 2=8,

the quarterly interest,

The regular deposit,

= 144.828 144.83

Jill should deposit approximately $144.83 at the end of each quarter.

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Solutions: Work Sheet 3

(a) APP [ /10] including the table in part (c)

Present value is: Interest rate = 6%

The interest rate compounded monthly is:

The number of payments is:

To determine the monthly payment, use the following formula :

So, monthly payment is

Note: this part is for part (e),or they can quote the value from amortization table

To find the total interest paid, we have:

Total amount paid for 5 years = = 2319936.18

Therefore, total interest = 2319936.18 - 2000000 = $ 319936.18

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(b) APP [ /10] including the table in part (d)

The loan is $ 2000000 but they are going to get 2% cash back

2% of 2,000,000 =

= $ 40,000

So, the present value (PV) of the loan = 2,000,000 - 40,000 PV = $ 1,960,000

The monthly interest rate (i) =

= 0.00625 The number of monthly payment (n) = = 72

Now we can calculate monthly payments by the formula;

By substituting the values PV = 1960000, i = 0.00625, n = 72

=

= 33,888.62

So, monthly payment is $ 3,388.62

Note: this part is for part (e),or they can quote the value from amortization. table

The total amount paid for 6 years = 2,439,980.64

Total interest = 2,439,980.64 - 1,960,000 = $ 479,980.64

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c) Amortization Table- Scotia Bank

Present value (Loan) 2000000Annual interest rate 0.06Amortization period (years) 5Monthly payment 38665.60Total payments 2319936

Payment Number Monthly Payment Interest PaidPresent

Value PaidOutstanding

Balance

0 2,000,000.001 38,665.60 10,000.00 28,665.60 1,971,334.402 38,665.60 9,856.67 28,808.93 1,942,525.473 38,665.60 9,712.63 28,952.97 1,913,572.504 38,665.60 9,567.86 29,097.74 1,884,474.765 38,665.60 9,422.37 29,243.23 1,855,231.53

…54 38,665.60 1,326.63 37,338.97 227,987.4855 38,665.60 1,139.94 37,525.66 190,461.8256 38,665.60 952.31 37,713.29 152,748.5357 38,665.60 763.74 37,901.86 114,846.6758 38,665.60 574.23 38,091.37 76,755.3059 38,665.60 383.78 38,281.82 38,473.4860 38,665.60 192.37 38,473.23 0.25

Total Paid Interest 319,936.25

d) Amortization Table- TD BankLoan 2000000CashBack 0.02Present value (Loan) 1960000Annual interest rate 0.075Amortization period (years) 6Monthly payment 33888.62Total payments 2439980.64

Payment Number Monthly Payment Interest PaidPresent Value

PaidOutstanding

Balance

0 1,960,000.001 33,888.62 12,250.00 21,638.62 1,938,361.382 33,888.62 12,114.76 21,773.86 1,916,587.523 33,888.62 11,978.67 21,909.95 1,894,677.574 33,888.62 11,841.73 22,046.89 1,872,630.685 33,888.62 11,703.94 22,184.68 1,850,446.00

…67 33,888.62 1,243.48 32,645.14 166,311.8368 33,888.62 1,039.45 32,849.17 133,462.6669 33,888.62 834.14 33,054.48 100,408.1870 33,888.62 627.55 33,261.07 67,147.1171 33,888.62 419.67 33,468.95 33,678.1672 33,888.62 210.49 33,678.13 0.03

Total Paid Interest 479,980.67

(f) Even though the TD Canada Trust Bank deal give 2% cash back and also the period the loan is to be paid is longer (6 years compared to 5 years), the interest they have to pay on the loan is bigger than that of Scotia Bank deal. Therefore, the Scotia Bank deal is better to consider. So I will recommend that the committee should consider the Scotia Bank deal. CO [ /5]

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Technology

MathPFinance.doc