Unit VII Decision Making in Finance Section D: Credit Card ...

Advanced Mathematical Decision Making

Unit VII, Section D Planning

2009¨C10 Pilot Materials, Subject to Revision

11/2/09

Unit VII

Decision Making in Finance

Section D: Credit Card Debt

Section Planning

Learning Outcomes

1. Students analyze the parts of a credit card statement and derive how the

calculations are made.

2. Students calculate the minimum payment on a credit card balance and the

length of repayment based on that minimum and recommend an alternate debt

repayment plan.

3. Students learn the difference between annual percentage rate and effective

annual rate with respect to credit card costs.

4. Students create an amortization model based on a set debt plan and analyze the

behavior of principal and interest with a constant payment.

5. Students analyze real-world scenarios involving credit card debt, present and

discuss their conclusions, and synthesize the results into solutions to life problems.

Student Expectations

(DM.10) Mathematical decision making in finance. The student creates and

analyzes mathematical models to make decisions related to earning,

investing, spending, and borrowing money.

The student is expected to:

(A)

determine, represent, and analyze mathematical models for various types

of income, such as commission, salary, and hourly wage, to determine the

best option for a given situation;

(B)

determine, represent, and analyze mathematical models for expenditures,

such as credit cards, auto financing, cell phone plans, and financial aid, to

determine the best option for a given situation; and

(C)

determine, represent, and analyze mathematical models and appropriate

representations (such as expected values or probability distributions) for

various types of loans and investments, such as savings plans and real

estate, to determine the best loan or investment plan for a given situation.

Time Management

This section takes at least two instructional days. This does not include any class time

dedicated to extension or reflection questions.

Charles A. Dana Center at

The University of Texas at Austin

VII-110

Advanced Mathematical Decision Making

Unit VII, Section D Planning

2009¨C10 Pilot Materials, Subject to Revision

11/2/09

Lesson VII.D.1 deals with examining and extrapolating the elements of credit card

debt. This lesson is supported by Student Activity Sheet 9 and takes one instructional

day. This is a good opportunity to review weighted averages and the interest formula

!

r$

A = P # 1+ &

n%

"

nt

as it relates to the exponential form y = a ? b x .

Lesson VII.D.2 deals with creating and analyzing the amortization model of debt

payments. Students then solve real-world scenarios involving credit card debt. This

lesson is supported by Student Activity Sheet 10 and takes one instructional day.

Prerequisite Skills

?

?

?

Exponential equations

Bar graphs

Weighted averages

Vocabulary

Academic: bar graph

Application: actual interest rate, amortization, annual percentage rate, average daily

balance, budget, credit, credit card, credit line, daily periodic rate, debit, effective

annual rate, finance charge, minimum payment, principal, statement

Materials

?

?

Graphing calculators

Spreadsheet software

Related Resources

?

Internet access for student data research and applications

Additional Background

Connections

Students should come into this course with a strong understanding of exponential

functions. In this section, students build on that understanding by using it as a model

for the effective annual rate (EAR). Students explore the key properties of the graph

for amortization and analyze the relationship between principal and interest.

Graphing calculators are important tools in this section, both in calculations and

confirmation of formulas used to determine elements of credit card finance.

Charles A. Dana Center at

The University of Texas at Austin

VII-111

Advanced Mathematical Decision Making

Unit VII, Section D Planning

2009¨C10 Pilot Materials, Subject to Revision

11/2/09

Instructional Strategies

This section offers multiple opportunities for students to work in pairs or small

groups. Students can share their small-group work during whole-class discussion to

solidify new learning. In addition, Student Activity Sheet 10 primarily deals with the

analyses of real- world scenarios, which are completed in groups with the teacher

facilitating a process called QuIPS (the Question, the Information, the Process, and

the Solution). Students present their findings and discuss the reasonableness of the

findings with the class. Finally, using QuIPS as a framework, students find a common

understanding and plan of action based on all the scenarios to apply to real-life

situations.

Things to Watch for

The discovery processes outlined in the lesson activities are crucial to student

understanding of the mechanics involved in modeling these daily real-life decisions.

Teachers should facilitate not only student retention of these skills but also discussion

of using the formulated math to make informed decisions.

The use of technology, in particular the Time Value of Money (TVM) Solver in the

graphing calculator, is invaluable in confirming and calculating intricate details of

credit card statements. Spreadsheet software helps students quickly calculate the

parts of an amortization table, freeing time for analysis and critical thinking.

Some scenarios do not provide enough information to solve the given problem, so

students must rely on previous knowledge and applied understanding to generate a

solution. Teachers are cautioned against providing too much facilitation because it

can hinder the critical-thinking process that students often lack in mathematical

instruction. Rather, students should be given guidance sparingly along their quest

through QuIPS. If necessary, students should be given more than the allotted one

instructional day to analyze and synthesize their conclusions.

Charles A. Dana Center at

The University of Texas at Austin

VII-112

Advanced Mathematical Decision Making

Unit VII, Section D Planning

2009¨C10 Pilot Materials, Subject to Revision

11/2/09

Lesson VII.D.1: Making Sense of Creditese

Opening the Lesson

Discuss when high interest rates are a benefit and when they are a detriment.

Framing Questions

Discuss the title of the lesson. Because contracts and legal documents contain so

many complicated and confusing words and phrases not seen in the daily use of the

English language, a new word was defined to describe the legal language¡ªlegalese.

Credit is the term for money borrowed from a bank or credit card company. How do

you think creditese applies?

Activities

During this lesson, students work in pairs for parts of the lesson and then come

together for whole-class discussions. At the end of the lesson, there are some

questions to check for understanding that students work on individually.

VII.D.1 Student Activity Sheet 9

Questions 1¨C3:

Teacher

demonstration.

Whole-class

discussion.

1. Discuss all parts of the credit card statement. Some students

may find it difficult to find information visually.

2. To calculate the average daily balance, students must begin by

adding the transactions in order. Remind them that there are

31 days in July. To find the final answer, however, they only

need to find the sum of the balances, each multiplied by the

number of days it occurs, and then divide by 31. This is a

weighted average, and you may need to review this concept

with students before they attempt Question 1.

weighted average =

value ? quantity + value ? quantity + ... + value ? quantity

1

1

2

2

n

n

total quantity

3. Use the following general formula for the daily periodic rate to

answer Question 2:

daily periodic rate =

APR

days in cycle

4. Use the following general formula for the minimum payment

due to answer Question 3:

minimum payment = new balance ? minimum payment percent

Make sure that students manipulate the formula to find the

missing value.

Charles A. Dana Center at

The University of Texas at Austin

VII-113

Advanced Mathematical Decision Making

Unit VII, Section D Planning

2009¨C10 Pilot Materials, Subject to Revision

11/2/09

5. Discuss the flip side of interest rates regarding debt.

? Who benefits when credit card companies use a daily rate?

Why? (The credit card companies benefit because the

compound interest is even greater.)

? Who benefits when credit card companies use a higher

minimum payment? (Consumers benefit because they are

paying off the credit card faster and spending less in

interest.)

Questions 4¨C6:

Teacher

demonstration.

1. Have students discuss how Question 4 is the reverse of

Question 3.

2. You may decide to use the compound interest formula or a

spreadsheet for calculating the number of payments needed.

Use of the TVM Solver, however, is highly recommended so that

more time can be used for critical thinking.

3. The following steps are for a TI-84 Plus Graphing Calculator:

? Press APPS and select Finance and then TVM Solver.

? Enter the interest rate as an annual percent for I%.

? Enter the principal for the present value.

? Enter the payment as a negative for PMT.

? Enter 0 for the future value.

? Enter 12 for P/Y (payments per year) and 365 for C/Y

(compound periods per year).

? Press 2ND and ENTER to solve for N.

Students may be curious about why the PMT: is END. Explain

that this calculates the interest payment at the end of each

compound period, as is done in real life and in the formulas.

Students may also be curious about why the PMT is negative.

Explain that the TVM Solver is cash flow based and calculates

money values in terms of how money flows in and out of a

person¡¯s wallet. You may need to explain why 12 is entered

for P/Y and 365 for C/Y.

4. When students calculate N, have them divide by 12 to find

the number of years. Have students round up to the nearest

year (regardless of rounding rules) to answer the question

of how long it will take to pay off debt. (If you stop paying

before the partial month, the debt still has a small balance

left.)

Charles A. Dana Center at

The University of Texas at Austin

VII-114

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