Math RWLO Template Title Placeholder

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 take- home 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 fixed- rate 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    12  12 2377.5528 A  360   567.79  0.055  4.1874 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.