Unit 1 WebQuest - Internet Project

What Does it Take to Buy a House?

Introduction | Task | Process | Guidance | Conclusion | Questions

Introduction

Would you like to buy your own house some day? Many people look forward to owning their own homes. In 2000, the U.S. Census Bureau found that the home ownership rate for the entire country was 66.2%. The table below shows the home ownership rates in the U.S. from 1900 through 2000.

Source: www.census.gov

In this project, you will be exploring how functions and equations relate to buying a home and your income.

The Task

You have just finished college or technical school and have selected a city in which you would like live. You want to be sure that you can get a good-paying job and be able to afford to buy a house. In this project, you will prepare a portfolio containing your research regarding a job and housing in your new location. You want to show the portfolio to some friends and relatives so they can help you to decide whether you are making a wise decision. If you prefer, you can prepare a Web page with this information that others can view. Be sure that your portfolio or Web page contains the following information:

* the name of the career you have chosen and the salary range that you can expect for the job in the city of your choice;

* information on housing in the city, such as the range of prices of houses for sale;

* calculations showing what you can afford to borrow to buy a home;

* information about a loan for the amount you intend to borrow. This should include a table showing the amount of the loan, the interest rate, the number of years of the loan, and the payments.

The Process

To successfully complete this project, you will need to complete the following items.

* Select a career that interests you. Then select at least one city in which you would like to live. If you prefer, you can select several cities and compare the salaries and housing. Search for the expected salary for this career in the city of your choice. For help, try these Web sites.

www.salary.com
www.collegegrad.com
www.itcareerhub.com
www.idealist.org/career.html
www.brint.com/jobs.htm#Salary

* Determine how much you can afford to spend on a home. Some lenders suggest that your monthly house payment should be no more then 25% of your gross monthly income. If you want help determining what you can afford, try this Web site.

www.interest.com/calculators/earn-home.shtml

* Search for homes in the location of your choice. Determine whether there are houses available in your price range. For help, try these Web sites.

www.homefair.com
www.homestore.com
www.newhomesearch.com
www.homebuilder.com

* After you have determined how much money you will need to borrow for a home, choose several interest rates and lengths of time for the repayment. Find your payment per month and obtain an amortization table. For help, try these Web sites.

www.interest.com
www.interestratecalculator.com
www.usatoday.com/money/calculat/mcfront.htm

* Be creative. Add some additional data, information, or even pictures to your portfolio or Web page.

Guidance

Here are some additional questions and ideas you may want to consider for your project.

1. What additional costs are involved in owning a home?
2. What other expenses must you budget for each month from your paycheck?
3. How do salaries vary from area to area in the United States ? Research and compare salaries for several areas.
4. How does the cost of homes vary from area to area in the United States ? Research and compare home prices for several areas.
5. What are the advantages and disadvantages of owning your own home?
6. How do various taxes affect your income? Consider federal income tax, state income tax, property tax, and sales taxes.
7. What type(s) of insurance must you purchase as a homeowner?
8. What are the advantages and disadvantages of longer–term versus shorter–term loans, for example, a 15 versus a 30–year loan?

Conclusion

Here are some ideas for concluding your project.

* Present your project to your class or at a family night.

* Present the information on a Web page. Have other students critique your project and help you to make improvements to your project.

* Write a one—page summary of your project, including what you have learned from researching this topic.

* Interview a loan officer at a bank or home–mortgage company. Find out why the amount of principle and interest paid varies over the period of the loan. Why do you pay more in interest in your payments at the beginning of the loan?

Questions

Lesson 1-3

Ms. Martin was researching the costs of financing $125,000 for a home. She found that the monthly payment for a 6.875% loan for 30 years would be $821.16 per month. She found that the monthly payment for a 6.875% loan for 20 years would be $959.77 per month.

1. Write and solve an equation to find the amount of interest she would pay altogether for the 30-year loan.
2. Write and solve an equation to find the amount of interest she would pay altogether for the 20-year loan.
3. For which loan would she pay less interest? How much would she save with that loan?
4. A loan officer tells Ms. Martin that her payment should be no more than 25% of her gross monthly income (income before taxes). How much must Ms. Martin's gross yearly salary be in order to borrow $125,000 for each loan?

Lesson 2–5

Refer to the Exercise in Lesson 1–3. Ms. Martin receives the following amortization table showing her first twelve payments for the $125,000 20-year loan at 6.875%. Each payment is $959.77. Column three shows the amount of each payment that is interest, column four shows the amount of each payment that is principal, and column five shows the loan balance.

1. Make a scatter plot of the data where the x-values are the payment number (column 1) and the y-values are the balance of the loan (column 5).
2. Write the equation for a line of fit for the scatter plot in Exercise 1. What does the slope represent?
3. This table shows the balance due on Ms. Martin's loan at the end of each year for 20 years. Make a scatter plot of the data where the x-values are the year numbers and the y-values are the balances due at the end of each year.

4. Write the equation for a line of fit for the scatter plot in Exercise 3. What does the slope represent?
5. Why are the equations of the lines in Exercise 2 and Exercise 4 different?
6. Consider the two scatter plots. Do you think a linear equation is a good model for each set of data? Why or why not?

Lesson 3–2

Mr. Pearson was researching loans for $150,000. He chose a rate of 6.25% for 15 years. Each payment is $1286.13. The table shows the balance for his loan at the end of each year.

1. Make a scatter plot for the data where the x-values are the year numbers and the y-values are the balances due at the end of each year. Find an equation for a best–fit line for the data.
2. Refer to the Exercises in Lesson 2–5. Mr. Pearson wants to know if his loan balance and Ms. Martin's loan balance will ever be approximately equal at the same time before the final payment is made. An equation for Ms. Martin's loan where x represents the year number and y represents the loan balance is y = -6089.8 x + 136,558. Determine when the balances will be the same, if ever.

Lesson 4–6

Two loan balances can be approximated by the equations given in the table. The time x is in years.

1. Use Cramer's Rule to find when the loan balances will be approximately the same for the two loans before the final payment is made.
2. What will the approximate balance of each loan be at that time?
3. Why might your estimate of the time when the loan balances will be the same be somewhat inaccurate?

Teacher Notes and Answers

What Does it Take to Buy a House?

TEACHER NOTES

In this project, students research salaries for a career of their choice and also the cost of buying a home and financing it. There are many interesting ideas to explore about loan repayment. Students will notice that more is paid in interest than principal at the beginning of a loan. They may also be interested in graphing the payment number versus the balance using only the first year's payments versus graphing the years paid versus the balance over the entire loan period. During the first year or so, the graph is very close to linear. However, if you consider the whole life of the loan, the graph is slightly curved and a linear regression no longer fits the data as well. Also, it is interesting to note what happens when you have a loan for the same amount of time but compare several interest rates and lengths of time for repayment. In this project, students should discover that there are many resources available on the Internet for locating jobs all over the U.S.

The Guidance section of the WebQuest contains questions that would be good for a whole-class discussion. If you prefer, have each student research one of the questions and add the information they find to the final presentation of their WebQuest.

Several Web sites are included in the project to help students in completing this WebQuest. Encourage students to find additional sites and to share those sites with other students.

Students will work on this project in Unit 1.

ANSWERS

LESSON 1-3

1. Sample answer: I = [(30(12)(821.16)] – 125,000 or 170,617.60
2. Sample answer: I = [(20(12)(959.77)] – 125,000 or 105,344.80
3. the 20–year loan; $65,272.80
4. for the 30-year loan: $39,415.68; for the 20-year loan: $46,068.96

LESSON 2–5

1.

2. Sample answer using a calculator regression: y = –251.43 x + 125,016; the slope represents the approximate amount of principle per month by which the balance is reduced.

3.

4. Sample answer using a calculator regression: y = –6089.8 x + 136,558; the slope represents the approximate amount of principle per year by which the balance is reduced.

5. In the equation for Exercise 2, x represents the month. In the equation for Exercise 4, x represents the year. Therefore, the slopes are quite different. Also, for Exercise 2, the payments for only the first year are considered. For Exercise 4, the payments for the entire loan are considered.

6. A linear model fits the data for the first year fairly well. When you consider the payments over the entire 20-year period, a linear model does not fit the data as well. There may be better models for the data over the entire loan period. In fact, a quadratic regression equation fits the second data set very well.

LESSON 3–2

1.

Sample equation using a calculator regression: y = –9884.5 x + 159,887

2. Using substitution, –9884.5 x + 159,887 = –6089.8 x + 136,558; 3794.7 x = 23,329; x ˜ 6; the balances will be approximately the same at about the end of the sixth year of payments.

LESSON 4–6

1. in about 7.1 years

2. about $149.645; about $149,513

3. The linear models for the data may not be as good as needed to be extremely accurate.