How Much Does This House Really Cost?
Project Overview
Buying a house could be the single largest financial purchase made in one’s life.
Unless you can pay for the entire cost of the house upfront, you will have to
obtain a mortgage which is the loan for the money borrowed to buy a house.
This project allows students to investigate how much they would actually pay for
a house through a 30-year fixed-rate mortgage, with interest included, after 30
years. In a fixed-rate mortgage, the interest rate remains the same for the entire
time the mortgage is paid.
Students will use a hypothetical mortgage amount and enter their geographic
living areas (state and nearest city to which they live) on a specified online
financial website to obtain current mortgage interest rates. These various rates
will be from dozens of nearby lending institutions. These rates are updated daily
on the website that will be used as a primary resource.
Students will calculate the monthly mortgage payment associated with this
mortgage using a given formula, their scientific or graphing calculator, and online
interest rates. Students will verify their result with the monthly payment supplied
online and calculate the total amount paid for the house at the end of the 30-year
mortgage, with interest included. Students will calculate the total amount of
interest paid for the house.
Lastly, students will compare these results with the analogous calculations for the
same mortgage, but over 10, 15, or 20 years. Students will also react to their
findings in writing at the end of the project.
1
Student Learning Objectives
Upon working through this RWLO, the student will be able to:

Access a specified financial information website and obtain daily
30-year fixed-rate mortgage rates from dozens of local lending
institutions.

Use one of the published rates with the supplied mortgage payment
formula to calculate the monthly mortgage payment for a specified
mortgage amount using a scientific or graphing calculator.

Compare the monthly mortgage payment calculated from the supplied
formula with the estimated monthly payment supplied online. Students
will check that these monthly payments match.

Calculate the total cost of the house, and consequently, the total
amount of interest paid over the life of the 30-year mortgage.

Compare these results with the analogous calculations for the same
mortgage, but over 10, 15, or 20 years.

React to their findings in writing at the end of the project.
2
Procedure
Time: Approximately 45-60 minutes
Required Materials: Internet access, scientific or graphing calculators, paper
and pencil.
Prerequisites: Familiarity with using the exponential features of scientific or
graphing calculators.
Implementation: This project is intended to be used in a setting where students
have internet access. It is intended that students will work together in small
groups. Students are encouraged to work together in their calculations and
discuss the results within their group. This project could be assigned as a takehome project if internet access is not available to the whole class.
Steps:
1. Break the class up into small groups with 3-4 students in each group.
2. Distribute the “Content Material” section of this project to each student.
3. Read the section “Project Overview” aloud to the class.
4. Give the students time to read the background and work through the given
example of calculating the mortgage payment on a 30-year fixed rate
mortgage of $100,000 with a rate of 5.5%. Be sure to assist each group
with the use of the scientific calculator as needed until each group has
verified the monthly mortgage payment of $567.79
5. Groups should proceed through the steps of the section “Group
Instructions”. These steps guide groups through the process of finding
daily interest rates, calculating monthly mortgage payments, the total cost
of a house at the end of the mortgage, and the total amount of interest
paid on the house. Groups also calculate similar amounts based on
mortgages of shorten time periods. Lastly, students will write their reaction
to the different answers they calculated for total costs of both the house
and interest paid on the house. Students can access the site
http://www.census.gov/const/www/newressalesindex.html to find the
average cost of new house sold in various U.S. regions to help choose a
reasonable mortgage amount to work with for this project.
Be sure to guide the groups through these steps, assisting as needed.
3
Content Material
PROJECT OVERVIEW
Buying a house could be the single largest financial purchase made in one’s life. Unless you can
pay for the entire cost of the house upfront, you will have to obtain a mortgage which is the loan
for the money borrowed to buy a house.
This project allows students to investigate how much they would actually pay for a house through
a 30-year fixed-rate mortgage, with interest included, after 30 years. In a fixed-rate mortgage, the
interest rate remains the same for the entire time the mortgage is paid.
Students will use a hypothetical mortgage amount and enter their geographic living areas (state
and nearest city to which they live) on a specified online financial website to obtain current
mortgage interest rates. These various rates will be from dozens of nearby lending institutions.
These rates are updated daily on the website that will be used as a primary resource.
Students will calculate the monthly mortgage payment associated with this mortgage using a
given formula, their scientific or graphing calculator, and online interest rates. Students will verify
their result with the monthly payment supplied online and calculate the total amount paid for the
house at the end of the 30-year mortgage, with interest included. Students will calculate the total
amount of interest paid for the house.
Lastly, students will compare these results with the analogous calculations for the same
mortgage, but over 10, 15, or 20 years. Students will also react to their findings in writing at the
end of the project.
BACKGROUND
The formula we’ll use to calculate mortgage payments is given below:
n
r 
r

P 1   
12  12
A 
n
r 

1    1
 12 
In this formula,
A = the estimated monthly mortgage payment.
P = the amount initially borrowed for the house.
r = the annual interest rate (expressed as a decimal).
n = the total number of monthly payments that will be made to pay the mortgage.
4
Let’s work through an example using this formula. Suppose you obtain a 30-year fixedrate mortgage for $100,000 at a rate of 5.5%. Then we have
P = 100,000 (the mortgage amount)
r = 0.055 (the interest rate expressed as a decimal)
n = 360. (30 years multiplied by 12 months gives 360 mortgage payments)
This gives
360
0.055
 0.055 
100,0001 
 
2377.5528
12 
12

A

 567.79
360
4.1874
 0.055 
1 
 1
12 

GROUP INSTRUCTIONS
1. Each group should access www.bankrate.com and click on the 30-year fixed mortgage
option.
2. Each group should enter a hypothetical amount of money that they will finance the
house with through this mortgage. Enter that amount online as well as below:
Amount of the mortgage: __________________
3. Groups can enter the hypothetical state in which they will obtain the mortgage,
followed by the nearest city in that state to which they live. Enter this online and below:
State, Nearest City: _______________________
4. Lastly, groups should choose the 30-year fixed rate mortgage option, with 0 points
selected – “points” are additional amounts of money paid to the lending institution which
are separate from the mortgage, but which are often associated with lower interest rates.
In this project, we will be using 0 points.
5. The site will provide mortgage interest rates from possibly dozens of lending
institutions which are nearby the city and state information provided above. Choose a
lending institution and the corresponding interest rate from the ones listed.
Lending Institution:_______________________
Quoted Interest Rate:___________
5
6. Lets’ calculate the estimated mortgage payment using the formula
n
r 
r

P 1   
12  12
.
A 
n
r 

1    1
 12 
Write down the values of the variables:
P = ___________
r = __________
n = __________
Calculate A with your calculator. Be sure to show the numerical results of evaluating
the numerator and denominator of this formula, as in the background example. Show
your work below:
What result did you get for A?
A = ________________
Be sure to verify that your result matches the estimated monthly mortgage payment
quoted by the lending institution your group chose.
7. How could you use the value of A to calculate the total cost of the house if all
mortgage payments were made monthly for the entire life of the mortgage? Show your
calculation and result below: (just for your information - in addition to a mortgage
payment, there will be additional taxes and insurance costs which are also typically paid
monthly.)
Total Cost of House: ___________________
6
8. How could you use your answer to #7 above to calculate the total amount of interest
paid on the house after paying the 30-year mortgage? Show your calculation and result
below:
Amount of interest paid: _________________
9. You will now consider how much the same house would cost, at the same interest rate,
but with a mortgage that has a shorter repayment time. Instead of a 30-year fixed rate
mortgage, you will consider one of the following: a 10-year, 15-year, or 20-year fixed
rate mortgage for the same amount used above, at the same interest rate. Using one of
these time periods, answer the following:
What type or mortgage will you consider? (10-year, 15-year, or 20-year) _______
What is the new estimated monthly mortgage payment? Show your work below.
A = _____________ (Be sure to verify this with the online quote)
7
10. Using the value for A calculated in #9, calculate the total cost of the house after the
life of the mortgage.
Total Cost of House: ___________________
11. Calculate the total amount of interest paid on the house using your result from #10.
Amount of interest paid: _________________
12. Now that you have calculated the total cost of a house that results from two different
mortgages, summarize your findings in a few sentences below. How could you use this
information in the future?
8
Assessment
This RWLO is intended to be given in groups. The sample rubric given below could be
used if the RWLO were assigned to individuals instead of groups.
Sample Rubric
Steps 1-5: Filling in the amount of the mortgage, state, nearest city, lending institution,
and quoted interest rate – 10 points
Step 6: Displaying a correct calculation for A, including the simplified numerator and
denominator - 20 points
Step 7: Calculating the total cost of the house – 10 points
Step 8: Calculating the total amount of interest paid on the house – 10 points
Step 9: Displaying a correct calculation for A, including the simplified numerator and
denominator, for either a 10-year, 15-year, or 20-year mortgage – 20 points
Step 10: Calculating the total cost of the house with this shorter-term mortgage – 10
points
Step 11: Calculating the total amount of interest paid on the house with this shorter-term
mortgage – 10 points
Step 12: Writing a cohesive reaction to the answers calculated in #7, 8, 10,
and 11 – 10 points
9
Links to Course Competencies
This RWLO is recommended to be incorporated into any mathematics course
requiring scientific or graphing calculators, and which covers either compound
interest or exponential functions:

Beginning Algebra through College Algebra

Precalculus

Topics/Concepts of Mathematics
Specifically, this RWLO meets the following course competencies:

Information and Quantitative Literacy: collecting data from a website and
writing written reactions in context.

Collaborative work

Use of a scientific or graphing calculator to evaluate formulas involving
exponents

Order of operations

Exposure to a real world application of compound interest
10
Supplementary Resources

www.bankrate.com : a website that supplies a wealth of financial
information, including daily interest rates.

http://www.bankrate.com/brm/green/mtg/basics1-intro.asp : a website
which gives a comparison of renting versus buying. Individual links to
chapters which explain mortgage basics and other facets of buying a
house are accessible here.

http://www.bankrate.com/brm/rate/calc_home.asp : a website which
provided online calculators which can be used to estimate monthly
mortgage payments, as well as other loan payments.

http://realestate.yahoo.com/re/financing/rates.html : a website similar to
the above. This can be used as a backup website in case bankrate.com is
not available for use.

http://www.census.gov/const/www/newressalesindex.html : a website that
can be used to find the average price of houses sold by different U.S.
regions.
11
Recommendations
Recommendations for Integration: This RWLO is suggested to be
incorporated in a group setting where 3-4 students work collaboratively.
Students/groups should be encouraged to work together in verifying their
calculations match the calculations posted online. Written and/or verbal reactions
to how much is actually paid for a house over the life of the mortgage (both for
the house and for interest) are strongly encouraged to be discussed in class.
Back-up: In the event that the website www.bankrate.com is inaccessible during
the project, the following back-up site can be used:
http://realestate.yahoo.com/re/financing/rates.html
Students can pick from several major cities of each state in the U.S., or use the
posted state/national average mortgage rates, as left to the individual discretion
of the instructor.
If both sites are down, the instructor is encouraged to supply rates from the
newspaper, or other source, which has been obtained as recently as possible.
12