Course Profile Mathematics of Personal Finance, Grade 11,
College Preparation, Catholic and Public
Unit
5: Home Sweet Home
Time: 20 hours
Activity 1 | Activity 2
| Activity 3 | Activity 4
| Activity 5
Students
investigate costs and make comparisons among various types of accommodations,
summarizing their findings in presentations. Common mortgage terminology is
introduced and the methods of mortgage interest compounding are explored.
Appropriate technology is used to calculate total interest and to determine the
time required to “pay off” a mortgage when specific mortgage features are
varied (i.e., payment frequency, amortization period, and payment amounts).
Students use mathematical analysis as a basis for sound accommodation
decision-making.
|
Activity |
Time |
Expectations |
Assessment |
Tasks |
|
1. Out On My Own |
150 min |
PFV.02, PFV.04, PF2.01, PF2.02, PF2.03, PF2.04, PF4.01, PF4.02, PF4.03, PF4.04 |
Knowledge/ Understanding Communication Thinking/Inquiry/ Problem Solving |
Explore accommodation alternatives in the context of moving out on their own |
|
2. Are You Ready to Buy? |
225 min |
CIV.03, CI3.05, CI3.06 |
Knowledge/ Understanding |
Develop understanding of mortgages and demonstrate this through a classroom simulation |
|
3. Table Talk |
300 min |
CIV.03, CI3.07, CI3.08 |
Application Thinking/Inquiry/ Problem Solving |
Investigate amortization tables and create using technology |
|
4. How’d They Do That? |
300 min |
CIV.03, PFV.04, CI3.09, CI3.10, PF4.05 |
Application Thinking/Inquiry/ Problem Solving |
Manipulate mortgage features to observe the effect on total interest paid |
|
5. Summative: Check It Out! |
225 min |
PFV.02, PFV.04, PF2.02, PF2.03, PF2.04, PF4.03, PF4.04, PF4.05 |
Thinking/Inquiry/ Problem Solving Communication |
Make an accommodation decision based on a specific scenario using mathematical justification |
Time: 150 minutes
Students
collect information from various sources on types of accommodation in a
specific community. Students collect and compare information on the cost of
university or college residence, rental accommodation and the purchase of a
home. Students present their researched options in the form of a written letter
to their parent/guardian(s).
Strand(s): Personal Finance Decisions
Overall
Expectations
PFV.02 -
determine, through investigation, the relative costs of renting an apartment
and buying a house;
PFV.04 -
demonstrate the ability to make informed decisions involving life situations.
Specific
Expectations
PF2.01 -
collect, organize, and analyse data involving the costs of various kinds of
accommodation in the community;
PF2.02 -
compare the costs of maintaining an apartment with the costs of maintaining a
house;
PF2.03 -
compare the advantages and disadvantages of renting accommodation with the
advantages and disadvantages of buying accommodation;
PF2.04 -
summarize the findings of investigations in effective presentations, blending
written and visual forms;
PF4.01 -
describe a decision involving a choice between alternatives (e.g., Which
program should I study at college? What car should I buy? Should I stay at home
or rent an apartment?);
PF4.02 -
collect relevant information related to the alternatives to be considered in
making a decision;
PF4.03 -
summarize the advantages and disadvantages of the alternatives to a decision
using lists and organization charts;
PF4.04 -
compare the alternatives by rating and ranking information and by applying
mathematical calculations and analysis, as appropriate (e.g., calculating loan
payments or interest rates; constructing graphs or tables), using technology.
·
Collect
local newspapers, real estate magazines, local housing guides, sample lease
agreements, etc.
·
Make
arrangements for the use of the Internet if possible.
·
Borrow
college and university calendars with residency information from the guidance
department.
·
Acquire
copies of a residential tenancy agreement (see Resources).
·
Obtain
brochures from financial institutions on mortgage information.
·
Sticky
notes (5/student) are recommended.
Teacher
Facilitation
·
Introduce
a discussion with students regarding the various decisions that would need to
be made if you were to leave home to go to college.
·
Lead
student discussion towards a focus on accommodation decisions.
·
Distribute
collected resources throughout classroom to allow students to explore options.
·
Provide
each student with five sticky notes.
·
Instruct
students to record five different accommodation options from the provided
resources with an estimated monthly cost on each sticky note.
·
Instructing
student groups of three or four to share their researched accommodations.
·
Suggest
that within their group the students move the sticky notes around to classify
them in some manner (cost, type, etc.).
·
Facilitate
a discussion on the possible classification system for these options. If
students have not proposed the option of buying, mention this possibility.
Conclude the discussion by grouping all of the sticky notes on the front board
into the following categories: college residence, renting off-campus or buying.
Suggest that within each type, options could be classified even further. For
example, within renting, options could include a division between single and
multiple bedroom units.
·
Instruct
students to use the cost information on the sticky note to establish an
“average” cost for each type of accommodation. For example, the average cost to
rent a 2-bedroom apartment is $785/month.
·
Instruct
students to compare their “average values” to the “average values” determined
by other groups. Discuss the reason for the difference.
·
Lead
a discussion as to the validity of their results. Have students consider how
they can achieve a more valid figure in the classroom (i.e., take averages
using more figures).
·
Instruct
students to combine all of their figures (by accommodation chart category) on
the front board and find an average.
·
Questions
to be considered during a discussion of the results: Are the rental figures
consistent regarding what utilities are included? What considerations (other
than cost) exist when making accommodation decisions? Discuss how the “average
values” may differ between different communities.
·
Provide
students with the headings for an “Accommodation Chart” and provide resources
for the completion of the chart. Suggested headings are: Type of Accommodation,
Advantages, Disadvantages, and Cost Structure.
·
Present
the following scenario: You have been discussing attending college far from
home with your parent/guardian(s). They have asked you where you are going to
live. You suspect that if you present solid arguments for a specific
accommodation choice that you have researched, they will assist you
financially. Write them a letter to communicate three specific accommodation
options, and your choice, with justification.
·
Provide
students with the assessment rubric for the assignment (Appendix 1.1).
Student
Activity
·
Discuss
and explore accommodation options should you leave home to go to college.
·
Identify
and investigate the details and costs of five accommodation choices using
resources from a college community. After communicating these investigated
alternatives to the class, participate in a class discussion to classify these
alternatives.
·
Based
on research by students in the class, determine the average monthly costs of
these accommodation types for this college community.
·
Use
this information as you develop a chart listing these accommodation types and
citing the advantages, disadvantages, and approximate cost structures involved
with each.
·
Through
a written letter of justification to your “parent(s)/guardian,” outline the
details of three accommodation alternatives and request your parents’ financial
support for one of these choices.
·
Assess
students’ Knowledge/Understanding by the quality of the information in their
“Accommodation Chart”.
·
Assess
Communication and Knowledge/Understanding by evaluating the “letter to the
parents” using the provided rubric (see Appendix 1.1).
·
Assess
students’ ability to work independently by observing the extent to which they
independently retrieve information and complete the accommodation chart using
provided resources.
Students
with poor handwriting are encouraged to type their letter to their parents.
http://osca.ouac.on.ca/res-c.htm
for residence and housing information for Ontario colleges
www.relocatecanada.com
for the National Guide for People Relocating
www.acaato.on.ca/colleges.html
for addresses and phone numbers for all of Ontario’s colleges
www.lawsmart.com/landlord.html
or www.ilrg.com/forms/lease.html for a tenancy agreement
http://www.realtylocator.com/inforesourcelocator.nsf/indexpagedisplay/resources!Opendocument
for real estate information around the world
Time: 225 minutes
Students
learn terminology associated with mortgages and develop an understanding of how
interest is calculated on mortgages in Canada. Graphing or financial calculator
technology is used to determine mortgage payments, while varying the
compounding period. Students use this knowledge to participate in a simulation
where they verbally justify to their parents (as a follow-up to Activity 1)
that they are prepared to be a homeowner.
Strand(s): Personal Finance Decisions
Overall
Expectations
CIV.03 -
demonstrate an understanding of the effect on investment and borrowing of
compounding interest.
Specific
Expectations
CI3.05 -
identify the common terminology and features associated with mortgages;
CI3.06 -
describe the manner in which interest is usually calculated on a mortgage (i.e.,
compounded semi-annually but calculated monthly) and compare this with the
method of interest compounded monthly and calculated monthly.
·
Prepare
“e-mail from the parents” (see Appendix 2.1) to introduce the lesson, and
provide structure to students for further research.
·
Gather
resources from banks, credit unions, mortgage brokers, etc. that list
information for consumers on mortgages. Most of these will include a glossary
which should include the following key terms: equity, mortgagor, mortgagee,
appraisal, term, principal, pre-approval, conventional mortgage, closing date,
interest rate, mortgage, payment frequency, amortization, offer to purchase,
portability, Canadian Mortgage and Housing Corporation (CMHC), closing costs,
land transfer tax, down payment, legal fees, etc.
·
Prepare
to deliver a brief lesson on the basic concept of compounding, as required.
·
Prepare
worksheet (see Worksheet 1) for students to determine monthly payments for
various mortgages, using both monthly and semi-annual compounding. The use of
the TVM Solver or the equivalent of any graphing or financial calculator is
suggested.
·
Prepare
index cards with three different scenarios. Each scenario includes a home
price, down payment amount, mortgage interest rate, and amortization period.
There should be a set of scenarios for each group of three students in the
class. These scenarios form the basis for the parent-student role-play that
completes this activity.
·
Prepare
“Student’s Understanding of Mortgages” assessment tool (see Appendix 2.2).
·
Graphing
or financial calculators are required for this activity. Student Worksheet 1
can be readily modified for use with any graphing or financial calculator.
Consult your owner’s manual for appropriate symbols.
Teacher
Facilitation
·
Provide
students with a hardcopy of the “e-mail” response sent by their parents as a
result of their letter in Activity 1 (see Appendix 2.1).
·
Use
this e-mail as a vehicle for communicating mortgage terminology to students that
they will be required to define in their own words. They are required to define
all of the underlined words in the letter. Provide resources (bank pamphlets,
flyers, dictionary) for students to research definitions.
·
As
a preparation for the upcoming “simulation,” demonstrate the use of the
graphing or financial calculator to calculate monthly payment. Explain the
symbols used on the calculator as they pertain to the mortgage terminology
definitions that the students have already explored. When compounding period is
explained, pose the question to students as to what kinds of compounding will
result in paying less interest.
·
After
students have predicted which compounding periods result in lower payments, go
through calculations together to (a) calculate monthly payments, and (b)
illustrate that semi-annual compounding results in lower payments than monthly
compounding. Let them explore this on their own and come to their own conclusion.
It would be more meaningful to them this way.
·
Students
may wish to explore various compounding periods other than monthly or
semi-annual, but it should be made clear that ALL mortgages in Canada have
interest that is compounded semi-annually but often paid monthly.
·
Assign
Worksheet 1.
·
As
a follow-up to the parent letter, explain that students are to participate in
an activity to “simulate” a conversation with their parent/guardian(s). Working
in a group of three, each student has the opportunity to convince the other two
“parents” that they are “home-ownership worthy.” Their arguments are based on
the information provided in their individual scenario card (each student in the
group has a different set of figures). When students pose as “parents”, they
provide feedback on the student’s arguments using a provided assessment tool
(see Appendix 2.2).
Student
Activity
In
response to the letter you wrote in Activity 1, your parents have written you a
detailed e-mail which includes a great deal of mortgage terminology. You learn
what these terms mean, and work through sample mortgage calculation problems
using a graphing or financial calculator. You will write a quiz to show what
you’ve learned. This work prepares you for a role play activity where you convince
two other students (posing as your parent/guardian(s)) that you are
knowledgeable of and ready for home ownership. Your “parents” will then give
you feedback on your ability to communicate your understanding.
Student
Worksheet 1
1. List the mortgage term that relates to each
of the following symbols:
N= I%=
PV= PMT=
FV= P/Y=
C/Y=
2. Complete the following chart using a
calculator with financial functions.
|
A |
For a mortgage amount of $105 000 at 8%/a interest amortized over 25 years |
|
|
N= I%= PV= FV= P/Y= |
||
|
Compounded Semi-Annually C/Y= PMT= |
Compounded Monthly C/Y= PMT= |
|
|
B |
Home purchased at $140 000 with a down payment of $20 000 at 7.4%/a interest amortized over 25 years. |
|
|
N= I%= PV= FV= P/Y= |
||
|
Compounded Semi-Annually C/Y= PMT= |
Compounded Monthly C/Y= PMT= |
|
|
C |
Home purchased at $125 000 with a down payment equal to 25% of the purchase price at 10.25%/a interest amortized over 20 years. |
|
|
N= I%= PV= FV= P/Y= |
||
|
Compounded Semi-Annually C/Y= PMT= |
Compounded Monthly C/Y= PMT= |
|
3. What should C/Y always be set at when working
with mortgages in Canada?
4. Calculate the monthly payments for each of
the following mortgages, assuming semi-annual compounding:
(a) $87 500 mortgage @ 9.85%/a amortized over 25
years
(b) $155 700 mortgage @ 8.90%/a amortized over 20
years, etc.
·
Assess
students’ Knowledge/Understanding by using the feedback from students in the
simulation (Student’s Understanding of Mortgages Assessment Tool)
·
Evaluate
students’ Knowledge/Understanding of mortgage terminology and calculations
using a quiz.
·
Assess
students’ initiative observing their participation in simulation (as both student
and parent).
Students
may be provided with the definitions of mortgage terms in list form.
Information on mortgage terminology can be found at the
following sites:
www.bmo.com/
(Bank of Montreal)
www.canadatrust.com
(Canada Trust)
www.cibc.com
(CIBC)
www.royalbank.com
(Royal Bank Financial Group)
www.tdbank.ca/
(Toronto Dominion)
www.cmhc-schl.gc.ca
(CMHC Canada Mortgage and Housing Corporation)
www.mortgagecentre.com/enter.cfm
(The mortgage centre)
www.canmortgage.com/
(Canada Mortgage)
For help with the TVM solver function of the TI83+
www.ti.com/calc/docs/act/83finch2.htm
For assistance with other brands of calculators:
CASIO – http://www-personal.umich.edu/~hjo/casio/
HP:
http://galaxy.einet.net/hytelnet/BBS009.html
SHARP:
call 1-800-BE-SHARP to order a calculator manual
TEXAS INSTRUMENTS:
http://navigation.helper.realnames.com/framer/1/112/default.asp?realname=Texas+Instruments+Calculators&url=http%3A%2F%2Fwww%2Eti%2Ecom%2Fcalc%2Fdocs%2Fcalchome%2Ehtml&frameid=1&providerid=112&uid=30005189 for calculator guidebooks
For a mortgage amortization calculator and other
information for this unit
http://finance.canada.com/bin/putform?Type=Calculator
Time: 300 minutes
Students
learn to complete calculations related to annuities and effective interest
rates to prepare for the game “Table Talk.” In this game, students make
calculations necessary to fill in incomplete monthly payment and monthly
interest tables. Students develop an understanding of mortgage interest when
they form and test a hypothesis for the total amount of interest paid over the
life of a specific mortgage. This understanding is reinforced when they learn
to interpret and generate amortization tables.
Strand(s): Personal Financial Decisions
Overall
Expectations
CIV.03 -
demonstrate an understanding of the effect on investment and borrowing of
compounding interest.
Specific
Expectations
CI3.07 -
generate an amortization table for a mortgage, using a spreadsheet or other
appropriate software;
CI3.08 -
calculate the total amount of interest paid over the life of a mortgage, using
a spreadsheet or other appropriate software, and compare the amount with the
original principal of the mortgage or value of the property.
·
Prepare
overhead of “Table Talk” Monthly Interest table (see Teacher Facilitation:
Interest on $1.00 Compounded Semi-annually)
·
Prepare
overhead of “Table Talk” Monthly Payment table (see Teacher Facilitation:
Blended Monthly Payment Table for a loan of $1 000)
·
Tables
reflecting the “Interest on $1.00 Compounded Semi-annually” will be required.
·
Prepare
overhead of complete amortization table.
·
Prepare
worksheet of incomplete amortization tables (Student Worksheet 1).
·
Secure
the use of one or more computers so that spreadsheet software can be employed.
Be prepared to provide review on basic spreadsheet use, as needed.
·
Local
resources regarding homes available for sale will be required (e.g.,
Newspapers, Internet, etc.)
Teacher
facilitation
·
Review
calculations involving annuity formulas and effective interest rates, as
needed.
·
Introduce
the game “Table Talk” and divide the class into two groups.
·
Present
the first “Table Talk” game board on the overhead. It reflects the interest on
$1.00 compounded semi-annually. A sample of a completed game board is provided
below. When used as a game board on the overhead, this table should appear
mostly blank. The figures below can serve as your answer key.
Interest
on $1.00, Compounded Semi-Annually
|
Time |
6% |
6.5% |
7% |
7.5% |
8% |
|
1 day |
.000161979 |
.000175265 |
.000188519 |
.00201741 |
.000214931 |
|
1 week |
.0011375235 |
.001230874 |
.001324008 |
.001416925 |
.001509627 |
|
1 month |
.004938622 |
.005344740 |
.005750040 |
.006154524 |
.006558197 |
Sample
Calculation (6% for 1 month)
(1.03)2
= (1+i)12
1+i = (1.03)2/12
i =
0.004938622
This
means that for any mortgage, one month of interest at 6% compounded
semi-annually would be equal to (0.004938622) x the outstanding principal.
For
example: A person’s outstanding balance on their mortgage (at a 6% rate) is $87
415.07. The interest portion of their payment for the next month would be: $87 415.07 x 0.004938622 = $431.71.
It should
be noted that from the time periods included in this table, the “1 month” time
is the only one used in amortization tables and is used most often. Time
periods of one day and one week are used to determine interest penalties or
interest charges for periods shorter than one month.
·
Complete
a calculation for one of the boxes on the game board as a class.
·
Identify
a team spokesperson to select a “box” for which the team would make the
calculation.
·
All
members of the team must reach a consensus on the answer before the answer is
presented.
·
The
team colour is used to shade in each box that is calculated correctly.
·
Each
time a team makes three calculations (diagonally, horizontally or vertically) a
point is earned.
·
When
the first game board is filled in, continue scoring using the “Table Talk”
blended monthly payment table. The completed table (below) is to be used as an
answer key; the game board presented to students is to be mostly blank.
Blended Monthly Payment Table (for a loan of $1000)
|
Amortization |
6% |
7% |
8% |
9% |
10% |
|
20 |
7.12189 |
7.69311 |
8.28358 |
8.89190 |
9.51665 |
|
25 |
6.39807 |
7.00416 |
7.63214 |
8.27978 |
8.94488 |
|
30 |
5.94824 |
6.58604 |
7.24712 |
7.92833 |
8.62668 |
Sample
Calculation (for 10% interest, amortized over 20 years)
Solve
for PMT in the formula for the present
value of an ordinary simple annuity.
PV =
PMT
Because
interest is compounded semi-annually and payments are made monthly, we can not
use this formula until we first make the compounding periods the same. To do
this, we calculate the effective monthly interest rate for 10% compounded
semi-annually.
(1.05)2
= (1 + i)12
i=.0081648461.
We can
then use this figure in the simple annuity formula PV = PMT [1-(1+i)-n/
i].
PV= 1000, i=.0081648461, n=20 12 = 240
ˆ PMT = 9.51665
·
Complete
a calculation for one of the game boxes as a class. The winning team is the one
with the greatest number of “tic-tac-toes” (three-coloured squares in a row).
·
Present
this “interesting scenario” to the class: Estimate how much total
interest is paid on a mortgage of $120 000, at an interest rate of 7% given
that interest is compounded semi-annually, amortized over 25 years.
·
Record
students’ estimates on the board to be revisited later.
·
Display
and explain a complete amortization table (as generated by a spreadsheet) for
this example.
·
Review
spreadsheet software by presenting the formulas that were required in the
spreadsheet to generate this amortization table.
·
Distribute
Worksheet 1 to provide opportunity for students to make amortization table
calculations.
·
Provide
resources for students to investigate homes that are available for sale in
their community. Instruct students to select one home they would like to
purchase in the future (in a price-range consistent with their anticipated
income established in unit one). The price of this home is to be used as the
mortgage amount.
·
Provide
three specific mortgage profiles for students to use (i.e., Interest rate 8.5%,
amortization= 20 years, etc.) Instruct students to apply their understanding of
amortization and spreadsheet software to generate an amortization table for
each mortgage profile.
Student
Activity
By
participating in the game “Table Talk,” you learn how to calculate the figures
found in various mortgage calculation tables. Using these tables in your
calculations, you learn to interpret, explain, and complete amortization
tables. You demonstrate this understanding through the completion of a worksheet.
Student
Worksheet 1
1. Determine the monthly payments using a
graphing/financial calculator or blended monthly payment tables for the
following:
a) $75
000 mortgage at 10.25%/a interest amortized over 25 years
b) $97
400 mortgage at 9.5%/a interest amortized over 20 years
2. Using an interest table for $1 compounded
semi-annually, determine the interest factor for a month and a week for the
following annual mortgage interest rates:
a) 8.75% b) 14.25% c) 12.5%
3. In each case below, determine the monthly
payment and the appropriate interest factor, then enter either “numerical data”
or “formulas” to complete the first four rows of each amortization table (DO
NOT complete the calculations by hand …use formulas)
a) A B C D E F
1 $70 000 mortgage @ 7%/a interest amortized
over 25 years
2 Interest factor is __________
3
4 Payment Monthly Interest Principal
5 No.
Payment Portion Portion Remaining
6 0
7 1
8 2
9 3
Now that
you have a better understanding of the total amount of interest paid during the
life of a mortgage, you will be required to create specific mortgage
amortization tables based on the purchase of a home in your community or your
future college community.
·
Use
student Worksheet 1 to assess students’ Knowledge/Understanding and Application
of spreadsheet and amortization table calculations.
·
Assess
Application by students’ ability to successfully produce amortization tables
for their chosen home.
·
Assess
teamwork by observing students’ interaction with classmates during the “Table
Talk” game.
Visually
impaired and/or learning disabled students may require an enlarged hardcopy of
the game boards.
For
financial calculators on the Internet go to:
http://www.financenter.com/calculate/all_calculate.fcs
Time: 300 minutes
Students
explore various mortgage features (i.e., payment frequency, amortization
period, alternative payment options, interest rates, etc) using appropriate
technology. Total interest will be compared when each option is varied, as well
as total time required to pay off the mortgage. Students analyse how these
different factors influence the total interest paid and the time required to
“pay off” the mortgage.
Strand(s): Personal Finance Decisions
Overall
Expectations
CIV.03 -
demonstrate an understanding of the effect on investment and borrowing of
compounding interest;
PFV.04 -
demonstrate the ability to make informed decisions involving life situations.
Specific
Expectations
CI3.09 -
compare the effects of various payment periods, payment amounts, and interest
rates on the length of time needed to pay off a mortgage;
CI3.10 -
demonstrate, through calculations, using technology, the effect on interest
paid of retiring a loan before it is due;
PF4.05 -
explain the process used in making a decision and justify the conclusions
reached.
·
Development
of amortization tables
·
Application
of interest and payment tables in developing spreadsheet formulas
·
Use
of graphing or financial calculators
·
Computers
are required for a portion of this activity, and graphing or financial
calculators are useful at all stages.
·
If
spreadsheets are unavailable, options include using a template of a spreadsheet
to allow for the set-up of an amortization table, or a data projector.
·
Create
a generic amortization table spreadsheet template to be made available to students.
·
The
classroom is divided into five stations, as described in the chart below. The
equipment for each station is to remain at each station throughout the
activity.
|
Station Number |
To compare the
effects of … |
Requirements |
|
1 |
Varying Payment Frequencies (monthly vs. weekly vs. accelerated weekly) |
Graphing/financial calculator for every student at this station. |
|
2 |
Varying Payment Frequencies (monthly vs. semi-monthly vs. bi-weekly) |
Graphing/financial calculator for every student at this station. |
|
3 |
Varying Amortization Period (20 vs. 25 vs. 30 years) |
Graphing/financial calculator for every student at this station. |
|
4 |
“Lump Sum” Payments |
Spreadsheet Software with file “station4” |
|
5 |
Payment Size (constant vs. payment increasing by a percentage) |
Spreadsheet Software with file “station5” |
·
For
stations 1-3, have the graphing/financial calculators set up at the appropriate
screen to perform required calculations.
·
For
station 4, prepare a spreadsheet amortization table for an $85 000 mortgage at
7.9%/a interest, amortized over 25 years, including a calculation for total
interest. Save as “station4.” The same file may be saved at station 5, but
saved as “station5.”
·
Worksheets
1 and 2 are designed to be adapted to the graphing/financial calculator being
used. See the owner’s manual of the specific calculator being used for
additional information.
Teacher
Facilitation
·
Provide
two scenarios, as illustrated below, to show how a more expensive home may end
up costing less over the life of a mortgage, based on mortgage features that
were utilized.
Example 1: $99 000 home, $10,000 down payment, 8.75%
interest, 25 year amortization, paid monthly. This leads to a monthly payment
of $722.34, and approximately $226 700 paid over the life of the mortgage
Example 2: $145 000 home, $10 000 down payment, 7.5%
interest, 20-year amortization, pay accelerated weekly. This leads to a monthly
payment of $1078.11, and an accelerated weekly payment of $269.53. Also, with
this scenario, the mortgagor is allowed to increase their weekly payment by 20%
starting the second year of the mortgage. Approximately $221 979 is paid over
the life of the mortgage
·
Initially,
share only the house price, and total money spent over the life of the
mortgage. Have students brainstorm how this could be possible.
·
Ask
students to brainstorm the factors that influence the total cost of a mortgage.
Guide students towards practical approaches (using mortgage features) that may
be used to lower mortgage costs. Allow students to explore these approaches by
changing the information on the spreadsheet template that has been prepared by
the teacher.
·
Demonstrate
the feature of the graphing or financial calculator which allows you to
determine the number of payment periods based on a given amortization period
and payment frequency
(see Student Worksheet 1).
·
Demonstrate
the calculation of payments for various payment frequencies based on the
monthly payment (see Student Worksheet 1).
·
Distribute
Student Worksheet 1 for completion.
·
Prepare
students for upcoming station activity by demonstrating examples using a
graphing or financial calculator or spreadsheet as a demo. Using a constant
mortgage amount and interest rate, complete the following as a class:
Example 1 (to prepare for stations 1 and 2)
Determine the monthly payment and total amount
paid (Payment x N); determine weekly payment (monthly * 12 /52), and determine
“N” using a graphing/financial calculator, and calculate total paid (weekly
payment x N). Compare the total amounts paid.
Example 2 (to prepare for station 3)
Determine monthly payment using 25 year
amortization, and calculate total amount paid over 300 payments; Determine
monthly payment using 20 year amortization, and total amount paid over 240
payments. Compare total amounts paid.
Example 3 (to prepare for station 4 and 5)
Using a spreadsheet, illustrate how to
calculate total interest for a given mortgage by adding all values in interest
column. Determine total paid by adding principal amount (and down payment if
known) to this total. Demonstrate how to increase payment by 5% (payment *
1.05) and enter this as the new payment illustrating the situation where a
mortgagor may increase their payments. Demonstrate again how to total the
interest paid, highlighting the fact that it will now take less time to pay off
the mortgage, and only those rows with positive interest values should be
added. Re-calculate the new total amount paid, and compare to the original
total.
·
Set
up the classroom with five types of stations (2 of each). See Planning Notes.
·
Provide
students with student Worksheet 2 to facilitate station work.
·
After
station work, re-group students and discuss conclusions that were drawn, as a
class, to insure correct conclusions have been drawn.
·
Challenge
students to a friendly exploration to see which group can find conditions
(within certain parameters) that will minimize the costs on a $150 000 home.
Suggested parameters are:
·
can
use an interest rate ¾% less than any advertised rate they can find
·
can
use either: lump sum payments (up to 10% of the principal remaining) once/year
OR several lump sum payments totalling no more than 10% of the principal at the
start of the year OR increasing the size of the monthly payment (no more than
double)
·
can
use other mortgage features.
·
To
apply these conclusions, each group will be given two homes with different
prices (keep within $30 000). Assuming both homes were purchased using the same
down payment, students are to vary mortgage features in each case to
demonstrate how it is possible to pay less in total for the more expensive home
than for the cheaper one. Remind students they may vary interest rates (no more
than 1.25% difference as a guide), amortization period, payment frequency, and
payment amounts. When complete, they should be able to describe the payment
plans established for each home, along with the total costs for each (see
Student Worksheet 3).
Student
Activity
Brainstorm
the ways that the total amount paid for a home varies depending on the mortgage
features selected. Review the use of a graphing or financial calculator to
determine unknown values such as payment, number of payment periods, etc. by
completing Student Worksheet 1.
Student
Worksheet 1 –
Determine missing values using graphing or financial calculator (students are
to complete columns 2 and 3). Additional examples may be added to assess
Knowledge/Understanding.
|
Given
Information |
Calculator
Values |
Missing
Information |
|
$85 000 mortgage @7.6% interest amortized over 20 years |
N= PMT= I%= FV= PV= P/Y= C/Y= |
Monthly payment = Semi-monthly payment = |
|
$115 000 mortgage @9.35% interest amortized over 25 years |
N= PMT= I%= FV= PV= P/Y= C/Y= |
Monthly payment = Accelerated weekly payment = Number of payments using accelerated weekly payment = |
Sample
Worksheet 2 How Do
The Features Affect Total Cost?
|
Use $85 000 mortgage @ 7.9% interest amortized over 25 years (unless told otherwise) N = I% = PV = PMT = ? FV = P/Y =12 C/Y =2 |
|||
|
Station 1 – compare monthly/weekly/accelerated-weekly payments with TI83 |
Monthly payment = ______ Total Paid = PMT x N = ______ |
Weekly Payment = ______ Using weekly PMT, value for “N” = ____ Total Paid = PMT x N = _______ |
Accelerated Weekly Payment = _______ Using accelerated weekly PMT, value for “N” = _________ Total Paid = PMT x N = ___________ |
|
Conclusion from Station 1 – |
|||
|
Station 2 – compare monthly/semi-monthly/bi-weekly payments with TI83 |
Monthly Payment = ________ Total Paid = PMT x N = __________ |
Semi-Monthly Payment = ________ Using semi-monthly PMT, value for Total paid = PMT x N = _________ |
Bi-weekly payment = _________ Using bi-weekly PMT, value for Total paid = PMT x N = ________ |
|
Conclusion from Station 2 – |
|||
|
Station 3 – Compare 25 year amortization to 20 or 30 year amortizations using TI83 |
25 year: N = ______ Monthly PMT = _____ Total Paid = PMT x N = ______ |
20 year: N = ______ Monthly PMT = _____ Total Paid = PMT x N = ________ |
30 year: N = _______ Monthly PMT = _____ Total Paid = PMT x N = _________ |
|
Conclusion from Station 3 – |
|||
|
Station 4 – Compare constant payments to “lump-sum” payments using a spreadsheet (for example add lump sum payments on every “anniversary date” of mortgage) |
(Open file “station4”) Monthly PMT = ____ Total Interest = _____ Total Paid = Principal + Interest = _______ |
-On every 12th payment, increase payment on spreadsheet by $1500 (i.e., at payment # 12, 24, 36, etc.) New total Interest paid = _______ New total Paid = ____ |
-On every 12th payment, increase payment on spreadsheet by $2500 -New total Interest paid = ________ New total paid = ________ (Close file. DO NOT save changes) |
|
Conclusion from Station 4 – |
|||
|
Station 5 – Compare constant payments to increasing payments by a percentage (for example, increase payments 2 years into the mortgage) |
(Open file “station5) Monthly PMT = _____ Total Interest = _____ Total Paid = Principal + Interest = ______ |
Increase PMT by 10% New PMT = ______In spreadsheet, change all payments to new increased PMT starting at payment 24 New Total Interest = __________ New Total Paid = ____ |
Increase original PMT by 15%: New PMT = ________ In spreadsheet, change all payments to new increased PMT starting at payment 24 New Total Interest = ___________ New Total Paid = _____ |
|
Conclusion from Station 5 – |
|||
Student
Worksheet 3
|
Two homes are purchased at $85 000 and $120 000, both using down payment of $10 000. Demonstrate how mortgage features may be selected so that the total amount paid for the $120 000 home will be less than the total amount paid for the $85 000 home. Any or all mortgage features may be different, but you may not vary the interest rate by more than 1.25%. |
|
|
$85 000 Home -Interest Rate: -Amortization Period: -Payment Frequency: -Payment Amount: -Changes to Payment Amounts: Total Interest Paid: Total Principal Paid: Total Paid Altogether: |
$120 000 Home -Interest Rate: -Amortization Period: -Payment Frequency: -Payment Amount: -Changes to Payment Amounts: Total Interest Paid: Total Principal Paid: Total Paid Altogether: |
·
Assess
Application by students’ ability to use technology to complete the missing
values at each station.
·
Assess
students’ Problem Solving by their ability to draw conclusions or trends for
each of the varying mortgage features (Summative Assessment).
·
Assess
Thinking/Inquiry/Problem Solving based on their arguments and justification
presented as a result of their exploration associated with Student Worksheet 3.
·
Assess
work habits as a result of their completion of Student Worksheet 3 and the
justification of their arguments.
As
indicated in students’ IEPs, students with learning disabilities may require
more time to complete this activity and to make their own conclusions. The
teacher may wish to assign fewer questions.
Time: 225 minutes
Students
develop a checklist designed to help individuals decide whether to rent or buy.
As a class, students explore the process of making an accommodation decision
and the various organizational tools that may be used (i.e., tables, lists,
etc.) to support such a decision. Accommodation alternatives for specific
scenarios are investigated and compared. Students make and present
accommodation decisions on these scenarios.
Overall
Expectations
PFV.02 -
determine, through investigation, the relative costs of renting an apartment
and buying a house;
PFV.04 -
demonstrate the ability to make informed decisions involving life situations.
Specific
Expectations
PF2.02 -
compare the costs of maintaining an apartment with the costs of maintaining a
house;
PF2.03 -
compare the advantages and disadvantages of renting accommodation with the
advantages and disadvantages of buying accommodation;
PF2.04 -
summarize the findings of investigations in effective presentations, blending
written and visual forms;
PF4.03 -
summarize the advantages and disadvantages of the alternatives to a decision
using lists and organization charts;
PF4.04 -
compare alternatives by rating and ranking information and by applying
mathematical calculations and analysis, as appropriate (e.g., calculating loan
payments or interest rates; constructing graphs or tables), using technology;
PF4.05 -
explain the process used in making a decision and justify the conclusions
reached.
·
Prepare
overheads/visual aids that display the use of tables, pros/cons lists, charts
and graphs as a support for decision-making.
·
The
use of graphing or financial calculators and spreadsheet software is required.
·
Prepare
two sets of family scenario cards: one set where the families would likely be
recommended to buy; another set where the families would likely be recommended
to rent. Renting scenarios may include situations where a family will stay for
a limited time period; an older couple who cannot maintain a home; a student
who does not have the time to maintain a home, or possibly a family or person
that cannot afford the costs of home ownership.
·
Community
resources on homes for sale and rental opportunities are required.
·
Availability
of the Internet is also desirable.
·
Poster
board, markers, and other supplies for students to create a visual display are
required.
Teacher
Facilitation
·
Instruct
pairs of students to generate ideas for a two-column checklist. “You Should Buy
If… and You Should Rent If” checklist. Completion of the checklist would give
guidance to an individual making accommodation decisions.
·
Encourage
students to share their ideas and develop one list as a class.
·
During
the discussion, relate to students some general information regarding the
financial requirements for mortgage approval. You may consider presenting
specific financial ratios (Total Debt Service Ratio [TDS]: the ratio of all
monthly expenses to gross monthly income should not exceed 40% and/or Gross
Debt Service Ratio [GDS]: the ratio of mortgage, taxes and heating to gross
monthly income should not exceed 32%.
·
Present
the class with a family scenario. For example: The Jones family has a total
income of
$85 000 and is moving to your area. They intend to stay here for some time,
given the fact that they have family here. They have about $5000 in savings.
The family has two kids, aged 15 and 17. (Note: add enough information
to allow students to make a decision)
·
Encourage
students’ input as to whether the family should rent or buy. Incorporate the
checklist created by the class into the discussion.
·
Time
permitting, work through another scenario as a class to reinforce the process
of problem solving: I lived in a condo and paid $1000 per month. I stayed there
for 4 years. If I had a down payment for a house, should I have bought? What
would I have to show for it? What equity would I have had today? What if I had
invested that down payment and lived in the condo? What would I have in the
bank?
·
Present
the various lists and organization charts that can be used to organize
information when making decisions: advantages/disadvantages chart or pros and
cons list, concept maps and mathematical calculations where appropriate.
·
Incorporate
these tools into the discussion, reinforcing their importance in the
decision-making process.
·
Emphasize
the decision-making process and the importance of justification wherever possible.
·
Present
each student with two scenario cards (one renting, one buying).
·
Instruct
students to research accommodation in their own community for the renting
family. Students are to thoroughly explore and present two accommodation
alternatives that best meet the needs of this family. They are to present a
final recommendation for just one of these two (with justification). The
picture of the accommodation and/or the advertisement is required as part of
the project.
·
The
same process is to be completed for the buying family scenario, although
specific details from mortgages available from community financial institutions
will need to be used. Students are to submit an amortization table based on
monthly payments, 25-year amortization, and interest rates posted in local
newspapers. They are also to explore realistic alternatives that may enable
this family to reduce the total interest paid. This may include: a lower
interest rate, different amortization period, different payment frequencies,
and/or altering payment amounts. Students are to justify why their chosen
alternatives are, in fact, realistic for the family in question. Using
technology wherever appropriate, students are to demonstrate the amount of
interest that this family could save as a result of the students’ suggestions.
Student
Activity
With a
partner, develop a checklist that would help people decide if they should rent
or buy. Working together with the class, create a final usable “checklist”.
Apply this checklist to two specific family scenarios. Using real housing data
in the community, select two viable accommodation alternatives for each family,
then use mathematical reasoning (with justification) to make one recommendation
for each family. Apply mathematical calculations (total monthly payment, total
interest paid, variations of mortgage features) and the use of technology the
analysis of each alternative. Using lists and organization charts, as well as
amortization tables, you develop a visual presentation of the recommendation to
each family.
Use the
rubric (see Appendices) to evaluate each students’ Problem Solving and
Communication skills independently.
Learning
Skills
Assess
students’ organization by their ability to organize their report and visual
presentation.
Additional
scaffolding (such as structured worksheets and/or specific suggestions for
strategies to lower interest costs) for this final project may be required.
Arrange for peer assistance for students with reading or writing disabilities
when preparing the visual presentation of renting versus buying.
For a
home financing calculator go to:
http://finance.canada.com/bin/putform?Type=Calculator
|
|
Level 1 (50 – 59%) |
Level 2 (60 – 69%) |
Level 3 (70 – 79%) |
Level 4 (80 – 100%) |
|
Knowledge/ Understanding Proposal detail |
- alternatives provide limited detail |
- alternatives provide some detail |
- alternatives provide considerable detail |
- alternatives provide thorough detail |
|
Accuracy of financial information for alternatives |
- limited accuracy |
- some accuracy |
- considerable accuracy |
- a high degree of accuracy |
|
Communication Use of correct mathematical terminology |
- limited correctness |
- some correctness |
- considerable correctness |
- a high degree of correctness |
|
Mathematical and written justification |
- limited mathematical/ written justification |
- some mathematical/ written justification |
- considerable mathematical/ written justification |
- convincing mathematical/ written justification |
Note: A student whose achievement is below
level 1 (50%) has not met the expectations for this assignment or activity.
Thanks
for the note about where you might like to live. It’s obvious from all of the
work you’ve done that you’re really growing up.
However,
you mentioned the possibility of “buying” a home. Are you sure you’re ready for
such a big commitment? I mean, when we were your age, we knew nothing about
buying a house. We didn’t know about mortgage brokers or that you could
go from bank to bank trying to get the best interest rate.
We’d
love to help you out with buying a home, if it’s the best choice, but we just
don’t want you to make the same mistakes that we did. If we had played our
cards right, we could have saved a bundle in interest. We didn’t make
any extra payments, we just paid the same monthly payment every month for 25
years. We were never told about things like: double up or lump sum
payments or different payment frequencies. We didn’t even know there
were amortization periods other than 25 years. Apparently, there’s some
new type of calculator that helps you make all kinds of calculations with
mortgages.
Also,
if we had realized all of the closing costs we would need to pay (in
addition to our down payment) such as legal fees, and land
transfer tax, we would have avoided many problems. All we were concerned
with was “Can we afford the monthly payment?” When the furnace broke
down, the unanticipated maintenance costs caused us to have to use milk
crates and the “floor” as our furniture for a while.
If you
can prove to us that you’re ready for this commitment and that you’re
knowledgeable of mortgages and home ownership issues, we will help you out. (Of
course, we’re going to need to know some numbers—like how much you’re going to
need up front). Let’s meet so that we can talk about these things further.
Use the
following form to assess _________________________ as they present to you, the
parent, their understanding and knowledge of home ownership. It is very
important that you read this over entirely before the student proceeds as you
play the role of the “parent”. Also, ensure that you assess fairly and honestly.
It will be very helpful to include detail where space is provided. Remember
that YOU will be evaluated on your thorough completion of this page.
1. Check off all mortgage terminology used in
the role-play and add any terms that are used but not listed here.
|
Accelerated payment |
Interest |
Monthly Payment |
|
Amortization period |
Interest Rate |
Mortgage Broker |
|
Closing costs |
Land Transfer Tax |
Payment Frequency |
|
Double-Up Payment |
Legal Fees |
Weekly Payment |
|
Down Payment |
Lump Sum Payment |
________________ |
|
_________________ |
__________________ |
________________ |
For
questions 2-6, circle the best response and add extra information if possible.
2. Were the terms used in the proper context?
(i.e., used properly in sentences, not just “listed”)
Never Not often at all Sometimes Usually Often All the time
0 1
2 3 4 5
Details: ________________________________________________________________
3. Did it appear from the explanations given
that the student understands these terms?
Not at all Just a little Mostly Almost
Totally Completely
0 1 2 3 4
Details: ________________________________________________________________
4. a) Was
the home price given? Yes No
1
0
b) Was the down payment given? Yes No
1 0
c) Was the monthly payment given? Yes No
1 0
d) Was the total of all closing costs given? Yes No
1 0
e) Was there an explanation for the values
above?
None Some,
not too clear Most, fairly clear All clearly explained
0 1 2 3
5. As the “parent”, are you convinced that your
child understands what they are getting into and deserve your support?
|
No way, wouldn’t |
Sort of, but |
Seems to |
Understand clearly |
|
lend them a nickel |
I’d still worry |
understand |
and is ready to be a homeowner |
|
0 |
1 |
2 |
3 |
6. List all evidence that they’ve “learned from
the parent mistakes” and would make better decisions. Each thing they would
change MUST include how it would help them in order to count.
Details:
_____________________________________________________________________
7. a) Was
a graphing or financial calculator used to demonstrate costs? Yes No
1 0
b) Did
the student explain the use of the graphing or financial calculator, including
what the values mean?
Not at all Very little Somewhat Pretty Well Very
Clearly
0 1 2 3 4
Details:
________________________________________________________________
|
|
Level 1 (50 – 59%) |
Level 2 (60 – 69%) |
Level 3 (70 – 79%) |
Level 4 (80 – 100%) |
|
Communication - use of terminology - clarity of presentation of alternatives |
- limited use of appropriate mathematical and mortgage terminology |
- some use of appropriate mathematical and mortgage terminology |
- considerable use of appropriate mathematical and mortgage terminology |
- consistent use of appropriate mathematical and mortgage terminology |
|
- presents alternatives for reducing total mortgage costs with limited clarity |
- presents alternatives for reducing total mortgage costs with some clarity |
- presents alternatives for reducing total mortgage costs with considerable clarity |
- clearly presents alternatives for reducing total mortgage costs with a high degree of clarity |
|
|
Problem Solving - reasoning - reasonableness of recommendation |
- presents argument and refers to amortization table to support argument with limited effectiveness |
- presents argument and uses amortization table to support argument with some effectiveness |
- presents argument and uses amortization table to support argument with considerable effectiveness |
- presents argument and uses amortization table to support argument with a high degree of effectiveness |
|
- recommendation offers limited realism as to the given family scenario |
- recommendation is somewhat realistic for the given family scenario |
- recommendation is considerably realistic for the given family scenario |
- recommendation is highly realistic for the given family scenario |
Note: A student whose achievement is below
level 1 (50%) has not met the expectations for this assignment or activity.
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