TITLE OF LEARNING EXPERIENCE: Using an Amortization Table

Author: Jennifer French

1LEARNING CONTEXT

This learning experience will connect the areas of mathematics, technology, occupational studies and social studies (economics). Students will learn about using an amortization table so that they can apply this information to make informed decisions when applying for loans. The students will need to have a basic understanding of decimals and operations involving them. Standards and benchmarks covered include:

MST #1: Students will use mathematical analysis, scientific inquiry, and engineering design, as appropriate, to pose questions, seek answers, and develop solutions.

• Students develop and present proposals including formal hypotheses to test their explanations, i.e., they predict what should be observed under specified conditions if the explanation is true.
• Students use various means of representing and organizing observations (e.g., diagrams, tables, charts, graphs, equations, matrices) and insightfully interpret the organized data.

MST #2: Students will access, generate, process, and transfer information using appropriate technologies.

• Students access, select, collate, and analyze information obtained from a wide range of sources such as research databases, foundations, organizations, national libraries, and electronic communication networks, including the Internet.

Occupational Studies #3A: Information management focuses on the ability to access and use information obtained from other people, community resources, and computer networks.

• Students use technology to acquire, organize and communicate information by entering, modifying, retrieving and storing data.

Social Studies (economics) . Economics requires the development and application of the skills needed to make informed and well-reasoned economic decisions in daily and national life.

• Students present economic information and conclusions in different formats, including graphic representations, computer models, research reports, and oral presentations.

2PROCEDURE

Students will use the Internet to find a site that contains an amortization table. They will use a search engine to find an amortization table. The table found at:

http://www.mainstmortgage.com/mortgagecalculators/amorttable/mainamort.html

will allow students to enter all their own information (principal, rate, and time). It will give them to identify the monthly payment, total interest paid and total cost of the loan.

Once the students have found this site, they will bookmark it for future reference. The teacher will then remind students about the relationships they have discovered having to do with compound interest. The teacher will ask the students to make hypothesis about the results of changing time and rate. The teacher will ask them to discuss with a partner the reasons why they made the hypothesis they did.

Students will then be given a guided practice form to obtain information. The students will closely examine the affects of time and rate on a mortgage. They will examine the different monthly payments that accompany the changes in time and rate. They will hopefully see that the monthly payment varies little between twenty and thirty year loans. The biggest difference they will see is in the final cost of the loan. The difference in total cost of a twenty and thirty year loan is tremendous. Guided questions will show students how much more a loan costs if it is taken out over longer periods of time, while the monthly payment between the two is minor.

3INTRUCTIONAL/ENVIRONMENTAL MODIFICATIONS

The classroom teacher will act as a facilitator for this lesson. The teacher will be able to work with individual, special needs students. The resource room students have additional support one period a day if necessary, as do the ESOL students.

4TIME REQUIRED

This lesson will take approximately two forty-three minute class periods to complete. The teacher must plan time prior to the lesson to verify that the amortization website is still available or to locate another one. There are many others to choose from.

5Resources

Access to the Internet, a computer lab with enough computers that students can work in groups of two or three, the website for the amortization chart, and the attached worksheets.

6ASSESSMENT PLAN

Describe the:

The teacher will continually circulate through the room and gather a general assessment of student understanding by asking questions such as "Why would there be so much more interest for a thirty year loan than a twenty year loan?" The assessment from this lesson will be a general check for correct information found in the worksheets.

A homework assignment should be given at the end of this lesson. The assignment would be a one page written consumers guide explaining the steps a consumer should take before borrowing money. It should include the reasons for each step and a general warning about the dangers of high interest, long length loans.

A more authentic assessment will take place in the culminating lesson of the Learning UNIT. At that time students will be asked to make judgements on payment plans and substantiate their choices with graphic data.

7STUDENT WORK

Send three or four samples of student work:

• that reflect different levels of student performance; and

• include comments reflecting the basis for teacher’s assessment.

8REFLECTION

Please offer personal comments on the learning experience:

• why this lesson was developed for the specific learning standard(s) and performance indicator(s);

• what you learned form implementing this lesson; and

• how the lesson was reviewed by peers prior to submission and what you learned from the review.

This lesson offers students the opportunity to gather a greater understanding of real world mathematics. The methods used to investigate the relationships in this lesson are explorative and systematic. The main objective is that after completing the lesson, students will be better able to make sensible decisions regarding mortgage loans. All work is to be completed under the supervision of the classroom teacher. A lot of group discussion will take place to help internalize the students’ findings. They will discuss the pros and cons of taking longer and shorter length loans. It is extremely important that the teacher do not force one choice as being correct. Some students and adults have a philosophy that living for the moment is more important than planning for the future. These students will most often choose to take longer loans so that they have more money in their pocket today to buy other things they want NOW. Other students would prefer to choose a shorter loan and live with less liquid assets now so that they will save a lot more money in the long run.

The most important aspect of this lesson is the fact that students can replicate the work at home if they have a computer and the Internet. This real world skill will become necessary to students when they begin making major purchases on bank loans. Students need to know they are somewhat in control before they go to the lending institution. They can determine ahead of time what the various costs will be so they can make informed decisions before they are put under pressure by a salesperson.

AMORTIZATION

In our last section we charged an amount of money, chose a variety of interest rates plus monthly payments and analyzed the relationships.

When buying a car, we usually borrow the money from a bank and pay it back in equal monthly payments, i.e., with a fixed rate loan. The length of the loan and the interest rate determine the monthly payment. These are set at the time that the money is borrowed and an Amortization schedule is set up. To amortize means to gradually extinguish.

Recall: on credit cards, time was somewhat of a hidden factor.

In this section, you will compare the effects of interest rate and time on the total cost and the monthly payment. There are some valuable lessons to be learned her that can save you a substantial amount later on in life.

Use the Amortization Table we found on the Internet to complete the following.

Suppose that you borrow $20,000.00 for a car and pay it off in 6 years.

Fill in the Chart below for the various interest rates.

Suppose that you borrow $15,000.00 for a car and pay it off in 6 years.

Fill in the Chart below for the various interest rates.

Suppose that you borrow $7,500 for a car and pay it off in 6 years.

Fill in the Chart below for the various interest rates.

The Effects of Time on Total Cost

Often, people stretch loans out for a long period of time. However, if they consider all factors they may find it in their best interests to borrow money for a shorter amount of time.

How much would you expect to repay on a loan for $25,000 over a period of 10 years?

If you extend the loan for 30 years, would you expect to pay more or less in the long run?

Explain why you think the loan should cost more or cost less.

Fill out the table below and draw your own conclusion.

AMOUNT $25,000.00

AMOUNT $50,000.00

AMOUNT $75,000.00

How much difference is there for a monthly payment between 15 and 30 years?

Would you be better off taking a loan for 15 or 30 years? Justify your answer in complete sentences.

How much difference is there for a monthly payment between 20 and 30 years?

Give reasons to support taking a loan for 20 years.

Give reasons to support taking a loan for 30 years.

When borrowing money, what factors should you consider when determining the terms of the loan?