Saving Time and Interest on your Home Mortgage Project Overview
Many times students question where, when, or how formulas discussed in class are used in the real world. This RWLO will provide students the opportunity to discover, first hand, how financial institutions use the monthly mortgage payment and mortgage amortization formulas. They will also learn the effect of making extra principal payments each month on both the length of the loan and amount of interest they will pay. A great life lesson for us all! Students will access the most current local interest rates available using the Internet. They will apply this rate to the formulas learned in class to determine their monthly house payment. After doing this, along with determining how much of the payment actually goes to principal, students will enter data into an Internet based mortgage calculator that will allow them to discover the effect of paying extra on their house payment. The RWLO should be used after a traditional presentation and practice using the formulas. It should be viewed as an enrichment exercise for students. After completing the worksheet, students should be required to report on their reactions to what they discovered. This should lead to some interesting classroom discussion.
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Student Learning Objectives
For this RWLO, the student will be able to: 1. Use the Internet to find current mortgage rate information. 2. Utilize a “real world” application of the Regular Monthly Payment formula and repayment schedule formula. 3. Demonstrate the ability to enter data properly and use an Internet-based mortgage payment calculator. 4. Discover the savings in time and interest realized when extra principal payments are made each month. 5. Report and discuss their findings.
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Procedure
Time: Approximately 60 minutes Materials: Computer, access to the Internet, pencil, paper, scientific calculator and the content materials worksheet. Prerequisites: Students should have an understanding of how to use exponents, order of operations, and formula evaluation. The assignment is intended as a concluding activity following a lesson and practice using the Monthly Payment Formula and repayment schedule formula. Implementation: This RWLO can be used either in the classroom, if computers are available, or as a homework project. Students should be administered a technology skills survey before the assignment is given. This will help in forming student partnerships. Steps: 1. Assign or have students choose a partner for this assignment. 2. If necessary, review the formulas for finding the monthly payment and repayment schedule. 3. Pass out the content materials including the instructions and worksheet. 4. Have students read the instructions and complete the worksheet activity, assisting as necessary. 5. Have students share and discuss their findings.
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Content Material
Student Directions: In this assignment, you and your partner will see how financial institutions use the mortgage formulas we have been working with in class. More importantly, you will discover the effect making regular extra monthly payments on your mortgage will have on the amount of interest you pay and the length of your loan. 1.) Using a computer connected to the Internet go to: www.bankrate.com and find the best rate available in (your city) for a 30 year, $150,000.00 fixedrate mortgage with 0 points. To do this, when you are at the site, under loan type, click on the 30-year fixed-rate. Enter 150,000.00 in the “financing for” space and choose (your state) for the state, click next. Choose (your city) for the city then click next. You want a 30-year fixed loan with 0 points, click next. Check for the best rate available(local banks will be in black, bold font). Rate found_____________ 2.) Using this rate and the Regular Monthly Payment Formula we have been using in class (below), find your monthly payment. Show your work. Monthly payment_____________
r r P 1 12 12 R 12t r 1 1 12
12 t
R = regular monthly payment P = principal amount r = interest rate (remember, expressed as a decimal) t = time in years
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3.) Following the steps below, determine the amount of your first months’ payment that will go towards the principal. How much will go towards the principal in the second month? Principal amount – month 1_____________ Principal amount – month 2_____________ Step 1 – Interest for the month = (old principal balance) x (annual interest rate) x (1/12 year). Step 2 – Payment on principal = (monthly payment) – (interest for the month) Step 3 – New principal balance = (old principal balance) – (payment on principal) Repeat this process for month 2. Remember the new principal balance found in step 3 becomes the old principal balance in step 1 the next month. Show your work.
4.) Now for the fun part. On your computer go to the website: http://www.moving.com/Mortgage_and_Finance/Calculators/PaymentCalc/
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Enter your $150,000.00 amount, annual interest rate and 30-year loan in the mortgage payment calculator. Click on submit. What is your monthly payment? Monthly payment_______________ Look at the amortization schedule. What amount goes toward the principal the first month? How about the second month? Month 1________________ Month 2________________ (Your answers for #4 should match your answers for #’s 2 and 3. Just checking your math!!) 5.) Click on the words “Full Amortization Schedule” located at the top right hand side of the amortization schedule for your loan results and scroll down to the end. How much interest will you pay over the 30-year loan?________________ What is the total you will pay for your house?_______________________ 6.) Using the “Back” button on your computer (twice), go back to the mortgage payment calculator page. Keeping your data the same, enter that you will pay an extra $100.00 monthly (in the Advanced Payment Method section). Submit. How much interest will you now pay?_________________ How much interest have you saved?_________________ How much sooner will you pay off your loan?___________ 7.) Repeat #6 using only a $50.00 a month extra payment. Interest paid?________________ Interest saved?_______________ Time saved?_________________ 8.) Feel free to experiment with any other extra payment amounts you wish!
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9.) Describe what you have discovered from this assignment. Do you think that making extra payments on your house is a good idea? Why or why not?
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Assessment
The intent of this assignment is for students to discover the benefits realized when we pay extra toward our mortgages. Since students have a tendency to complete assignments that have point values attached to them, the following rubric is presented as a suggestion only. Point values can be changed or modified at the instructors’ discretion. Question # 1 2 3 4 5 6 7 8 9 Total points Points 1 2 4 (2 points each) 3 (1 point each) 2 (1point each) 3 (1 point each) 3 (1 point each) – 2 10
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Links to Course Competencies
This RWLO could be applied in the following courses: Applied Algebra, Consumer Mathematics, Business Math and others. The RWLO addresses the following math competencies:
Formula evaluation Use of a calculator/computer to assist in problem solving Computer awareness Applying skills that involve algebra
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Supplementary Resources
The websites identified in the RWLO are recommended because they are very user-friendly regarding ease of navigation, entering data, and reading results. Other sites that could be used at the instructors discretion are: http://www.amo-mortgage.com/payment.html http://mortgages.interest.com/content/calculators/index.asp
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Recommendations
Recommendations for Integration: Since students may have varying comfort levels with using a computer and the Internet, this RWLO should be assigned to pairs of students or groups of three at the instructors’ discretion. It should be assigned as an out of class homework project if computer availability is an issue. Working with a partner or in a small group could also provide for better student reports and classroom discussion. This RWLO will provide students in an Applied Algebra, Consumer Mathematics, or Business Math class insight to a real world application of Algebra. Any of the other websites listed under supplementary resources could be used as a backup in the event the primary sites are not available.
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