Modeling Credit Card Debt (Modeling Module)

Author: Marsha Davis & Megan Heenehan

The content for this module is modeling credit card debt. The module begins with a Preliminary Reading, Credit Card Debt in America, which presents statistics on credit card debt and introduces Annual Percentage Rate (APR), used in calculating the cost of carrying a credit card balance. This is followed by a Preliminary Activity, Paying Off a $500 Purchase, in which students calculate the interest costs for putting a $500 iPad on a credit card.

In Activity 1, Recursive Models for Paying Off Credit Card Debt, students calculate monthly balances for two situations involving credit card debt, a small debt charged to a retail credit card and a sizable debt charged to a bank credit card. They use the patterns from their calculations of these balances to create a recursive model for calculating Bn+1, the balance in month n + 1, from Bn, the balance in month n.

For Activity 2, Spreadsheets to the Rescue, students find that spreadsheets are ideal for applying recursive models to generate credit card balances over many months. They use spreadsheets to compare how long it would take to pay off a large debt under different fixed monthly payments.

In Activity 3, Adapting Models to New Situations, students adapt their models to account for changes in the underlying assumptions on which their original models were based. Students adapt their recursive models to account for a missed payment, changes in the APR, and charging additional purchases.

Note: The information below was created with the assistance of AI.

Recommended Mathematics Level: Grades 9–12, primarily Algebra I/Algebra II, with portions accessible to advanced middle school students. The activity begins with percentages, decimal conversions, and simple interest calculations, then progresses to recursive formulas, sequences, spreadsheets, graphs, and adapting mathematical models. The authors specifically identify percentages and basic spreadsheet familiarity as prerequisites and list recursive modeling and spreadsheet implementation as core mathematical content.

Category	Summary
Application Areas	Personal finance/financial literacy: credit cards, debt, APR, interest, minimum payments, residual interest, budgeting, and repayment strategies. Mathematical modeling: creating, testing, evaluating, and modifying models as assumptions change. Technology/data analysis: spreadsheets are used to perform repeated calculations, organize results, and graph changing balances. Decision making: students compare payment amounts and APRs and evaluate the financial consequences of different choices.
Prerequisites	Calculating percentages; converting percentages to decimals; basic arithmetic with decimals; understanding variables and simple algebraic expressions/equations; basic spreadsheet skills or willingness to learn them. The document explicitly lists percentage calculations and basic spreadsheet use as prerequisites.
Primary Subject Matter	Annual Percentage Rate (APR); monthly interest rates; interest calculations; credit-card balances; recursive sequences/models; formulas such as determining the next balance from the previous balance; tables and spreadsheets; graphing balance versus time; comparing repayment scenarios; model assumptions; sensitivity to payment amount, APR, missed payments, additional purchases, and timing of purchases.
Mathematical Modeling	Students first calculate balances manually, identify a pattern, and generalize the pattern into a recursive model. They then use spreadsheets to extend the model over many months and compare repayment alternatives. Finally, they revise models when assumptions change, including missed payments, changing APRs, and additional purchases.
Technology	Excel is the primary tool, although the teacher notes indicate that Desmos or Python can also be used. Students implement recursive formulas, create tables, calculate many iterations, and produce graphs.

Correlation to Mathematics Standards

The document does not provide a formal standards alignment, so the following is a content-based correlation to the Common Core State Standards for Mathematics (CCSSM).

High School Algebra — Creating Equations (A-CED): Students create equations and formulas representing relationships among balance, interest rate, payments, and time and modify these equations as conditions change.

High School Functions — Linear, Exponential, and Recursive Relationships (F-IF/F-BF): Students represent changing credit-card balances recursively, interpret values in context, generate sequences from recursive rules, and examine how parameter changes affect outputs. The activity explicitly describes a recursive model in which each new balance is calculated from the previous balance.

High School Modeling: The lesson strongly addresses the CCSS modeling cycle. Students identify assumptions, construct a model, calculate results, interpret them in a financial context, evaluate the reasonableness of the model, and revise it when assumptions change. The activity explicitly emphasizes simplifying a situation first and then adding complexity when needed.

Standards for Mathematical Practice: Particularly strong connections include MP1 Make sense of problems and persevere; MP2 Reason abstractly and quantitatively; MP3 Construct viable arguments; MP4 Model with mathematics; MP5 Use appropriate tools strategically; MP6 Attend to precision; and MP8 Look for and express regularity in repeated reasoning.

Overall Assessment

Modeling Credit Card Debt is best classified as a high-school Algebra/Mathematical Modeling and Financial Literacy activity for approximately grades 9–12. Its strongest mathematical emphasis is not merely calculating interest, but developing, implementing, interpreting, and adapting recursive mathematical models. Students move naturally from arithmetic and percentages into algebraic modeling, technology-assisted computation, graphical interpretation, and quantitative decision making. The real-world credit-card context makes the material especially appropriate for Algebra I/II, quantitative reasoning, financial mathematics, or a mathematical modeling course.