Author Nina Riggs Background Information Lesson Reviewer Content Grade Level Unit/Cluster Lesson Topic Arra Chung Financial Literacy and Algebra 1 Grades 9-12 Algebra Unit Alignment: Linear and Exponential Relationships Credit Cards and Interest Rates Essential Questions: When and how is mathematics used in solving real world problems? How can linear and exponential relationships be used to analyze credit card debts? What characteristics of problems determine how to model the situation and develop a problem solving strategy? What factors contribute to rising credit card debt, and how can these factors be used to minimize debt? Why is it necessary to follow set rules/procedures/properties when manipulating numeric or algebraic expressions? How do interest rates, payments, fees, and charges impact credit card debt? Essential Questions and Enduring Understandings Enduring Understandings: Mathematics can be used to solve real world problems and can be used to communicate solutions to stakeholders. Fiscally responsible consumers can apply knowledge of interest rates, payments, fees, and charges to minimize credit card debt and maximize credit ratings. Relationships between quantities can be represented symbolically, numerically, graphically and verbally in the exploration of real world situations. Fiscally responsible consumers can use graphs, equations, tables, and numerical representations to analyze credit card statements and make informed decisions for paying down debt. Relationships can be described and generalizations made for mathematical situations that have numbers or objects that repeat in predictable ways. Analyzing interest rates, fees, and minimum payments can help consumers predict payoff time lines to make informed, financially responsible decisions regarding debt management. June 2016 Page 1 of 26
Background Information Focus Key Mathematical Practices: Make sense of problems and persevere in solving them. The students will make sense of credit card statements, annual percentage rates, payments, and long range affects of credit card debt. Reason abstractly and quantitatively. The students will quantitatively analyze payoff time lines for credit card debt, while taking into account fees and interest rates. Use appropriate tools strategically. The students will use graphing calculators and Excel to analyze credit card debt and payments to determine payoff time lines and long range affects of credit card charges. Across-Grade Coherence: Content Knowledge from Earlier Grades This lesson connects to the prior learning of percent of a number, from Grade 6 (6.RP.A.3). Coherence Within-Grade Coherence: Content from Other Standards in the Same Grade that Provide Reinforcement Students apply their learning of displaying data on a scatterplot (HSS.ID.B.6) and fitting a function by plotting and analyzing patterns and correlation coefficients (HSS.ID.B.6.B, C; HSS.ID.C.8). The students use these functions to analyze the data and extrapolate data, content learned with HSF.IF.A.2. The students apply their knowledge of linear and exponential relationships (HSF.LEA.A.1) to identify the relationship between the variables considered with credit card debt. Procedural Skill Calculate interest rates, annual percentage rates, minimum payment, and balance. Rigor Conceptual Understanding Determine the time it takes to pay off an accrued credit card balance. Understand the effects of interest rates, fees, and minimum payments. Modeling/Application Model credit card balances and payments over time using linear and exponential functions. June 2016 Page 2 of 26
Background Information Maryland College and Career Ready Standards Algebra I HSA.SSE.A.1.B Interpret complicated expressions by viewing one or more of their parts as a single entity. HSA.CED.A.1 Create equations and inequalities in one variable and use them to solve problems. HSF.BF.A.1 Write a function that describes a relationship between two quantities. HSF.BF.A.2 Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. HSF.LE.A.1 Distinguish between situations that can be modeled with linear functions and with exponential functions. HSF.LE.A.2 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). Student Outcomes Personal Financial Literacy Standards Make Inform, Financially Responsible Decisions 1.12.A Evaluate the financial choices that are made based on available resources, needs, and wants for goods and services. 1.12.B Evaluate attitudes, assumptions, and patterns of behavior regarding financial decisions, and predict how they impact the achievement of financial goals. Plan and Manage Money 3.12.B Analyze the services of financial institutions. Manage Credit and Debt 4.12.B Evaluate the advantages and disadvantages of credit products and services. 4.12.D Use numeracy skills to calculate the cost of borrowing. 4.12.E Identify and evaluate interest rates, fees, and other credit charges. 4.12.G Evaluate the consequences of not meeting credit obligations. Method for determining student readiness for the lesson How will evidence of student prior knowledge be determined? The Warm-up included in this lesson provides a means of determining which students possess the prior knowledge needed to be ready for this lesson. What will be done for students who are not ready for the lesson? Provide activities from online resources such as Khan Academy to refresh student knowledge on lines of best fit, exponential regression, and percent of a number. June 2016 Page 3 of 26
Warm Up Component Materials PARCC Formula Reference Sheet Graphing calculator Learning Experience Details Implementation Have the students answer the following questions about compound interest. The purpose of these questions is to engage their thinking with interest, debt, exponential growth, and rates. 1. Martha takes out a student loan of $2,500. The loan has an interest rate of 4.29% compounded yearly. How much will Martha owe after four years? [$2957.40] 2. Martha invests $2,500 into an account with 4.29% annual interest. If she leaves the money in the account for four years, how much interest will she earn at the end of the four years? [$429] Standards for Mathematical Practice Make sense of problems and persevere in solving them In this warm-up exercise, the students determine what formula to use in a financial scenario incorporating linear and exponential relationships. For English Language Learners Highlight key words such as rate, interest, compounded, debt, invest, etc. Provide the formulas for each exercise, writing out the formula in words as well as with variables. Provide bilingual dictionaries or online translation tools. June 2016 Page 4 of 26
Motivation Component Learning Experience Details Pose the questions, What is a credit card? Why would someone use or need a credit card? Allow the students to share their reasonings. (Possible responses: to establish credit, purchase items, consolidate bills.) Present the following picture: Standards for Mathematical Practice Construct viable arguments and critique the reasoning of others. The students present their argument(s) about the purpose and need for credit, and what considerations are needed when taking on debt through credit. Activity 1 Key Questions How do annual percentage rate, interest, fees, cash advances, credit line, minimum payment, prime rate, etc. impact your credit card balance? How do the introductory interest rate and the APR affect your credit card balance? What happens to your monthly payment throughout the first year? When do you think you will pay off your credit card? Ask, Which credit card would you apply for? Why? What information would you want to know about the credit card before applying for one? Why? Materials Needed Credit card (cut out for each student) Credit card agreement (copy for each student). Samples: o https://www.bankofamerica.com/credit-cards/credit-card-agreements.go o http://www.consumerfinance.gov/credit-cards/knowbeforeyouowe/ o https://www.discover.com/credit-cards/cardmemberagreement/index.html?icmpgn=agree_lhn_home_txt Implementation Provide the students with a credit card and a credit card agreement. Set a credit card limit for all the students. Allow them time to shop online. Point out that the only stipulation is they must keep under their credit limit. Note that some students may choose to spend the entire credit amount. Use these students as key examples later in the lesson when the students explore how long it takes to pay off the debt. Review the credit card agreement with the students. Define key terminology, such as Annual Percentage Rate, Interest, fees, Cash Advances, Credit Line, Minimum Payment, Prime Rate, etc. How does each of these items impact your credit card balance? Use appropriate tools strategically In this first activity, the students have complete access to the internet. Allow the students to explore theses online resources, which include dictionaries (to reference words in the agreement they may not know the definition of), translators (for English language learners so they can interpret the wording of the agreement), and for shopping for the most economical purchases. June 2016 Page 5 of 26
Component How would the payments, percentages, and balance be affected if you continued to make purchases with your credit card? How would the fees change if you paid more than the minimum payment? Formative Assessment Observe the entries in the table to assess student understanding of interest rates and monthly payments. Analyze the student responses to the questions included at the end of the Credit Card Table. Summary Reflect back on the charts created using the key questions. Analyze the amount of debt that remains after two years with respect to the initial credit card balance. Consider the effects of the interest amounts and minimum payments if charges were continually made. Learning Experience Details Explore what happens to the students credit card balances after two years. Create a chart similar to the one shown below. (Reference the sample answers provided in the resource materials.) Month Minimum Monthly Payment ( 2%) Introductory Interest Rate (14.9%) (+) APR (18%)* (+) 1 $0 2 $0 3 $0 4 $0 Credit Card Balance *Note: Annual Percentage Rate will not be calculated until after Month 12. Summarize Activity 1 by analyzing the chart created. Have students answer the following questions. (Reference the sample answers provided in the resource materials.) o How do the introductory interest rate and the APR affect your credit card balance? o What happens to your monthly payment throughout the first year? o When do you think you will pay off your credit card? o How would the payments, percentages, and balance be affected if you continued to make purchases with your credit card? o How would the fees change if you paid more than the minimum payment? Universal Design for Learning (UDL) Connections Using a table to organize the various charges within a credit card provides a connection to UDL Principle I Provide Multiple Means of Representation. Checkpoint 3.2 Highlight patterns, critical features, big ideas, and relationships http://www.udlcenter.org/implementation/examples/examples3_2 Standards for Mathematical Practice Reason abstractly and quantitatively The students work with their credit card balances, reasoning how interest rates, APR, and payments affect their overall balance. June 2016 Page 6 of 26
Component Learning Experience Details For English Language Learners Allow the students to use online translators to interpret the credit card agreement. Note that it is important that the students understand the wording of the agreement, and they should strategically access the same tools they would have access to in the real world. Make bilingual dictionaries available for the students, as the vocabulary in this activity is challenging. Standards for Mathematical Practice Activity 2 Key Questions o After how many months will your debt fall below $20? o When will you finally pay off your debt? o How much more did you end up spending on the items you originally purchased, once your credit card payments are taken into account? o How would your charging habits change if you knew then what you know now? Formative Assessment Generate a class discussion about the effects of various fees in credit card accounts. Utilize these key questions to assess student understanding of fees and credit card debt: How would these fees affect your scatterplots Materials Student generated charts from Activity 1 Graphing calculators or graphing software Implementation Have the students create scatterplot relating their minimum monthly payment with respect to the month, the credit card balance with respect to the month, and the minimum monthly payment with respect to the balance. Write linear functions and exponential functions that best model the data plotted. Use these functions to analyze the students debt. After how many months will your debt fall below $20? When will you finally pay off your debt? How much more did you end up spending on the items you originally purchased, once your credit card payments are taken into account? How would your charging habits change if you knew then what you know now? Generate a class discussion about the effects of late payment fees on interest rates, APRs, and credit card balance. Include a discussion on over credit limit fees and subsequent consequences. How would these fees affect your scatterplots and your functions? What function transformations would you see in your graph because of these fees (i.e. horizontal or vertical translation, dilation or reduction)? Test the student conjectures by having them calculate a late payment fee and an over the limit fee within their first year transactions. Summarize Activity 2 by analyzing the patterns formed by the graphs and the resulting functions generated. What happens to your balance over the years? [Sample answer: the balance slowly decreases.] Were you surprised by how long it would take to pay off your credit card? [Sample answer: Yes, paying only the Construct viable arguments and critique the reasoning of others The students analyze the effects of fees on their credit card debt, and determine the graphical transformations that result from these fees. Model with mathematics In this second activity, the students create scatterplots and write functions to model their credit card debt. Look for and make use of structure The students determine the function that best models the patterns within their credit card debt, and use these functions to extrapolate values. June 2016 Page 7 of 26
Component and your functions? What function transformations would you see in your graph because of these fees (i.e. horizontal or vertical translation, dilation or reduction)? Summary Analyze the patterns formed by the graphs and the resulting functions generated using these key questions: What happens to your balance over the years? Were you surprised by how long it would take to pay off your credit card? How would your graphs and functions change if you paid more than the minimum payment? How would your graph function change if you paid less than the minimum payment? How would your graph function change if you skipped a payment? Activity 3 Learning Experience Details minimum balance has little effect on paying off the overall debt.] How would your graphs and functions change if you paid more than the minimum payment? [Sample answer: The average rate of change would increase because the debt/balance is decreasing quicker. The slope would be steeper. The x-intercept would be lower for the linear function.] How would your graph function change if you paid less than the minimum payment? [Sample answer: The average rate of change would decrease because the debt/balance is decreasing more slowly or could possibly increase because of late fees. The x-intercept would be higher for the linear function.] How would your graph function change if you skipped a payment? [Sample answer: The average rate of change would decrease because the debt/balance is decreasing more slowly or could possibly increase because of late fees. The x-intercept would be higher for the linear function.] Universal Design for Learning (UDL) Connections Constructing graphs and functions to model the credit card payments and balances provides a connection to UDL Principle II Provide Multiple Means of Action and Expression Checkpoint 5.2 Use multiple tools for construction and composition. http://www.udlcenter.org/implementation/examples/examples5_2 For English Language Learners Allow the students to work in small cooperative learning groups. Provide bilingual dictionaries or access to online translators to facilitate the interpretation of such words as debt, fees, interest rates, transformations, etc. Standards for Mathematical Practice Materials Reason abstractly and Student generated charts from Activity 1. quantitatively Key Questions Sample credit card agreement In this last activity, the June 2016 Page 8 of 26
Component What have you learned about credit card debt? What are advantages and disadvantages to having a credit card? What is good credit? What is bad credit? Why is establishing good credit important? What techniques would help you to establish good credit? If you had followed the 20-10 Rule in your original charging adventure, what would be your net annual income and your monthly net income? Formative Assessment Assess the student understanding of credit card interest rates by comparing standard interest rates to those made on cash advances. Ask the following key questions to assess and solidify understanding: Why would someone need a cash advance? How are the fees for cash advances different from making a purchase Learning Experience June 2016 Page 9 of 26 Details Implementation Engage the students by asking the question, What have you learned about credit card debt? What are advantages and disadvantages to having a credit card? [Sample answer: Advantages are to build and establish a credit rating, to build a good reputation for handling debt and credit. Disadvantages are falling into debt that cannot be repaid, accruing late fees, building bad credit ratings which may prevent purchases such as a home or car.] What is good credit? [Sample answer: a 700-800 credit rating, a history of being on time with payments, and paying more than the minimum payment, keeping credit card balances at almost zero.] What is bad credit? [Sample answer: a credit rating below 600, a history of late payments and over the limit fees, high balance to credit card limit ratio.] Why is establishing good credit important? [Sample answer: to make purchases such as a home or car with low APR.] What techniques would help you to establish good credit? [Sample answer: pay on time, pay more than the minimum payment, keep balance low.] Use these opening questions to introduce other credit card topics, such as the 20-10 rule. Ask, What do you think might be the 20 and the 10 in the 20-10 Rule? Identify this rule of thumb as a means to keeping credit card debt within a person s affordable means. Use this rule to caution the students against borrowing more than 20% of their annual net income and 10% of their monthly net income. Challenge the students to answer the question, If you had followed the 20-10 Rule in your original charging adventure, what would be your net annual income and your monthly net income? Present a sample credit card agreement. Invite a student to read a description of cash advances. Why would someone need a cash advance? How are the fees for cash advances different from making a purchase with a credit card? How are the limits on cash advances the same or different from credit card limits? Reflect on your credit card charges. How would your table, graph and functions change if you had made cash advances? When a credit card is used for purchases, cash advances, and balance transfers, are monthly payments applied to all lines of credit or just one? What happens to the other lines credit if payments apply only to one line? Have the students experiment with this. Summarize Activity 3 by emphasizing how people can easily be trapped into Standards for Mathematical Practice students reason quantitatively about the 20-10 Rule. Construct viable arguments and critique the reasoning of others The students analyze cash advances and how the differing fees affect credit card debt, and determine the graphical transformations that result from these transactions.
Component with a credit card? How are the limits on cash advances the same or different from credit card limits? How would your table, graph and functions change if you had made cash advances? When a credit card is used for purchases, cash advances, and balance transfers, are monthly payments applied to all lines of credit or just one? What happens to the other lines credit if payments apply only to one line? Summary Explain to the students that when people use credit cards for multiple purposes (i.e. making purchases, getting cash advances, and transferring balances), it s like having multiple lines of credit on one card. Thus, if someone is making only the minimum payments, then that payment is not necessarily being applied to all of the lines credit. So, the interest on the other lines of Learning Experience Details high credit card balances to which minimum payments have little affect when cash advances and balance transfers are made. Explain to the students that when people use credit cards for multiple purposes (i.e. making purchases, getting cash advances, and transferring balances), it s like having multiple lines of credit on one card. Thus, if someone is making only the minimum payments, then that payment is not necessarily being applied to all of the lines credit. So, the interest on the other lines of credit (cash advances or balance transfers) continues to accumulate as if no payment is being made on them. These other lines of credit tend to have a separate, higher APR. It s a dangerous pitfall for people if they are not aware of it. Universal Design for Learning (UDL) Connections Continually referencing and working with the student generated charts from Activity 1 provides a connection to UDL Principle III Provide Multiple Means of Engagement Checkpoint 7.1 Optimize individual choice and autonomy http://www.udlcenter.org/implementation/examples/examples7_1 For English Language Learners Include contextual clues while reading about cash advances. Present concrete examples of how a cash advance would be obtained and why one would be needed. Provide bilingual dictionaries or access to online translators to facilitate the interpretation of such words as debt, fees, interest rates, advances, etc. Standards for Mathematical Practice June 2016 Page 10 of 26
Component credit (cash advances or balance transfers) continues to accumulate as if no payment is being made on them. These other lines of credit tend to have a separate, higher APR. It s a dangerous pitfall for people if they are not aware of it. Learning Experience Details Standards for Mathematical Practice June 2016 Page 11 of 26
Component Materials Poster paper Learning Experience Details Standards for Mathematical Practice Closure Implementation Summarize what the students have learned about credit cards and credit card debts. Have the students share out what amounts they charged and how long it would take them to pay off their debt. Divide the class into small groups. Direct the groups to generate a list of responsible credit card habits on a piece of poster paper. Responses may include: o Do not charge more than your limit. o Pay the entire monthly balance to avoid paying interest. If that is not possible, then pay more than the minimum payment. o Pay on time. o Avoid unnecessary charges and frivolous cash advances. Add additional cautionary advice to the students list, such as: o Be sure to understand the credit card agreement. o Know your interest rates and APR. o Notify the credit card company if you cannot pay your monthly payments. o o Report your lost or stolen card immediately. Never give out your card number over the phone or internet unless you know for certain who you are talking to and what you are buying. Universal Design for Learning Connections Understanding the advantages and disadvantages of credit cards and purposefully planning how to make credit work in ones favor provides a connection to UDL Principle II Provide Multiple Means of Action and Expression Checkpoint 6.2 Support planning and strategy development http://www.udlcenter.org/implementation/examples/examples6_2 June 2016 Page 12 of 26
Interventions/Enrichments Students with Disabilities/Struggling Learners English Language Learners Gifted and Talented Supporting Information Students with Disabilities/Struggling Learners: Create a note taking organizer (such as a Foldable) to help the students organize the vocabulary in the unit. Transfer the key questions from the Activities to a Cornell Notes format. Provide these notes to the students to help guide them through the lesson, focus them to the key concepts, and organize their notes. English Language Learners: Provide bilingual dictionaries or access to online translators to facilitate the interpretation of the vocabulary in the unit. Transfer the key questions and vocabulary from the Activities to a Cornell Notes format. Provide these notes to the students to help guide them through the lesson, focus them to the key concepts, and organize their notes. Gifted and Talented Students: Create a public service announcement for graduating students to caution them on the dangers of credit card debt as they head off onto their path of college and/or career. Include the positive aspects of credit cards, as well. Use voice threads, videos, webpages, etc. to create the announcement. Materials Copies of Credit Cards resource sheet Poster paper Technology Resources Internet access Graphing calculators https://www.bankofamerica.com/credit-cards/credit-card-agreements.go http://www.consumerfinance.gov/credit-cards/knowbeforeyouowe/ https://www.discover.com/credit-cards/cardmember-agreement/index.html?icmpgn=agree_lhn_home_txt June 2016 Page 13 of 26
Type I: Tasks that assess concepts, skills and procedures. Evidence Statement Most Relevant Standards Most Relevant Standards for Mathematical Practice Item Description and Assessment Qualities Scoring Information Evaluate attitudes, assumptions, and patterns of behavior regarding financial decisions, and predict how they impact the achievement of financial goals. Evaluate the advantages and disadvantages of credit products and services. Use numeracy skills to calculate the cost of borrowing. Identify and evaluate interest rates, fees, and other credit charges. Create equations and inequalities in one variable and use them to solve problems. Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). Maryland s College and Career Ready Standards Algebra I HSA.CED.A.1 Create equations and inequalities in one variable and use them to solve problems. HSF.BF.A.2 Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. HSF.LE.A.2 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). Personal Financial Literacy Standards Make Inform, Financially Responsible Decisions Manage Credit and Debt Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. This item assesses student knowledge of minimum payments on credit cards, and how interest rates can affect long range payments. See question below. Answer: C Points: 1 June 2016 Page 14 of 26
Jordan purchased a smart TV for $1,000 with her credit card. Her credit card company requires her to pay a monthly minimum payment of 3% of the outstanding balance or $15, whichever is greater. Her credit contract agreement includes a 22.9% annual percentage interest rate. Approximately how long it will take Jordan to pay off her credit card balance if she only pays the minimum required payment and makes no additional purchases? A. 1 year B. 5 years C. 10 years D. 12 years June 2016 Page 15 of 26
Type II: Tasks that assess mathematical reasoning. Evidence Statement Most Relevant Standards Most Relevant Standards for Mathematical Practice Item Description and Assessment Qualities Analyze the services of financial institutions. Use numeracy skills to calculate the cost of borrowing. Identify and evaluate interest rates, fees, and other credit charges. Create equations and inequalities in one variable and use them to solve problems. Write a function that describes a relationship between two quantities. Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. Distinguish between situations that can be modeled with linear functions and with exponential functions. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). Maryland s College and Career Ready Standards Algebra I HSA.CED.A.1 Create equations and inequalities in one variable and use them to solve problems. HSF.BF.A.1 Write a function that describes a relationship between two quantities. HSF.BF.A.2 Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. HSF.LE.A.1 Distinguish between situations that can be modeled with linear functions and with exponential functions. HSF.LE.A.2 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). Personal Financial Literacy Standards Make Inform, Financially Responsible Decisions Plan and Manage Money Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Use appropriate tools strategically. This question assesses the student s ability to recognize the exponential relationship between interest rates, monthly payments, and credit card balances. June 2016 Page 16 of 26
Scoring Information Part A Answers will vary slightly but should resemble the function Points: 1 Part B Answers will vary slightly but should be approximately $1770. Points: 1 Use the information provided to answer Part A and Part B for the question. Marc has maxed out his credit card, reaching his credit card limit of $5,000. The credit card company freezes his account, requiring him to pay the minimum payment of the card balance each month until the balance is paid off. Part A The graph below shows Marc s debt payoff over the years after his account is frozen. Balance Years Create a function that can be used to predict the balance, B(n) of Marc s credit card after n years. Part B Use your function to determine what Marc s credit card balance will be after 62 months of payments. June 2016 Page 17 of 26
Evidence Statements Most Relevant Standards Most Relevant Standards for Mathematical Practice Type III: Tasks that assess modeling/application. Evaluate attitudes, assumptions, and patterns of behavior regarding financial decisions, and predict how they impact the achievement of financial goals. Evaluate the relationship among income, spending decisions and lifestyle. Analyze the services of financial institutions. Evaluate the advantages and disadvantages of credit products and services. Use numeracy skills to calculate the cost of borrowing. Identify and evaluate interest rates, fees, and other credit charges. Evaluate the consequences of not meeting credit obligations. Create equations and inequalities in one variable and use them to solve problems. Write a function that describes a relationship between two quantities. Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. Distinguish between situations that can be modeled with linear functions and with exponential functions. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). Common Core Mathematics Standards HSA.CED.A.1 Create equations and inequalities in one variable and use them to solve problems. HSF.BF.A.1 Write a function that describes a relationship between two quantities. HSF.BF.A.2 Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. HSF.LE.A.1 Distinguish between situations that can be modeled with linear functions and with exponential functions. HSF.LE.A.2 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). Personal Financial Literacy Standards Plan and Manage Money Manage Credit and Debt Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Use appropriate tools strategically. Construct viable arguments and critique the reasoning of others. June 2016 Page 18 of 26
Item Description and Assessment Qualities Scoring Information Type III: Tasks that assess modeling/application. In this mathematical task, the students use numeracy skills to calculate the cost of borrowing. They add transactions to a credit card and identify and evaluate interest rates, fees, and other credit charges that occur based on the additional transactions. The students summarize their calculations by evaluating the consequences of charging various amounts to credit cards with high percentage rates. Answers will vary. Student responses should include the following elements: o A Credit Limit and two transactions within the credit limit set. o Correct Interest Charge Calculation after the new transactions. o o o Correct new minimum monthly payment after the new transactions and interest charges are added. Explanation of how the credit card company calculates the Approximate Time to Pay Off Statement Balance for both the minimum payment and $66. Identification on how the pay off of these amounts will change with the two new transactions and how much is saved by paying $66 instead of the minimum payment. Identification of how the Interest Charge Calculation, minimum payments, and Pay Off time change with cash advances Points: 2 per bullet June 2016 Page 19 of 26
Samuel is reviewing his monthly credit card statement, shown below: ANYBANK USA Manage your account online: www.anybankusa.com Additional contact information conveniently located on reverse side July 24 Aug 23, 2015 31 Days in Billing Cycle ACCOUNT SUMMARY PAYMENT INFORMATION Previous Balance $ 1721.91 New Balance $1,716.93 Payments and Credits - $ 50.00 Minimum Payment Due $50.00 Fees and Interest Charged + $ 33.58 Payment Due Date Sep 20, 2015 Transactions + $ 11.44 Late Payment Warning: If we do not receive your minimum payment by the date New Balance $ 1,716.93 listed above, you may have to pay up to a $35.00 late fee and your APRs may be Cash Advanced Credit Limit $ 500.00 increased up to the Penalty APR of 29.40% Credit Limit: $ Minimum Payment Warning: If you make only the minimum payment each period, Available Credit $ you will pay more in interest, and it will take you longer to pay off your balance. For example: Available Credit for Cash Advances $ Payment Amount Each Period If No Additional Charges Are Made INTEREST CHARGE CALCULATION Your Annual Percentage Rate (APR) is the annual interest rate on your account. Type of Balance Annual Percentage Rate (APR) Balance Subject to Interest Rate Interest Charge Purchases 22.90%P $1,726.73 $33.58 Cash Advances 24.90%P $0.00 $0.00 Approximate Time to Pay Off Statement Balance Estimated Total Cost Minimum Payment 15 Years $4,461.00 $66 3 Years $2,389.00 Your estimated savings if you pay off this balance is 3 years: $2,072.00 June 2016 Page 20 of 26
Use this information about Samuel s credit card to complete the following task: Set a Credit Limit for Samuel. Create two transactions Samuel could make within this credit limit you set. Recalculate the Interest Charge Calculation after these new transactions. Find Samuel s new minimum monthly payment after the new transactions and interest charges are added. Explain how the credit card company calculates the Approximate Time to Pay Off Statement Balance for both the minimum payment and $66. Identify how the pay off of these amounts will change with the two new transactions Samuel makes and how much Samuel will save by paying $66 instead of the minimum payment. Samuel has a $500.00 Cash Advance limit available. Have Samuel make a cash advance that is below this limit. Identify how will the Interest Charge Calculation, minimum payments, and Pay Off time change if Samuel makes this cash advance? Based on your calculations in this task, what advice would you give Samuel about making purchases and getting cash advances with credits cards? Use mathematics and your knowledge of the effects of credit card debt to support your reasoning. June 2016 Page 21 of 26
Student Credit Cards Directions: Make copies of the credit cards below. Cut out the credit cards and give one to each student. The credit card template is available for noncommercial use on Google Images.
Credit Card Table - Student Copy (For use with Activity 1) Initial Credit Card Balance: Month Minimum Monthly Payment ( 2%) Introductory Interest Rate (14.9%) (+) APR (18%)* (+) 1 $0 2 $0 3 $0 4 $0 5 $0 6 $0 7 $0 8 $0 9 $0 10 $0 11 $0 12 $0 13 14 15 16 17 18 19 20 21 22 23 24 Credit Card Balance
Credit Card Table Reflection Questions Using your Credit Card Table, answer the following questions: 1. How do the introductory interest rate and the APR affect your credit card balance? 2. What happens to your monthly payment throughout the first year? 3. When do you think you will pay off your credit card? 4. How would the payments, percentages, and balance be affected if you continued to make purchases with your credit card? 5. How would the fees change if you paid more than the minimum payment?
Credit Card Table Sample Student Response (For use with Activity 1) Initial Credit Card Balance: $2500 Month Minimum Monthly Payment ( 2%) Introductory Interest Rate (14.9%) (+) APR (18%)* (+) Credit Card Balance 1 $50 +$31.04 $0 $2481.04 2 $49.62 +$30.81 $0 $2462.23 3 $49.24 +$30.57 $0 $2443.56 4 $48.87 +$30.34 $0 $2425.02 5 $48.50 +$30.11 $0 $2406.64 6 $48.13 +$29.88 $0 $2388.38 7 $47.77 +$29.66 $0 $2370.27 8 $47.41 +$29.43 $0 $2352.29 9 $47.05 +$29.21 $0 $2334.46 10 $46.69 +$28.99 $0 $2316.76 11 $46.34 +$28.77 $0 $2299.19 12 $45.98 +$28.55 $0 $2281.75 13 $45.64 $0 +$34.23 $2270.34 14 $45.41 $0 +$34.06 $2258.99 15 $45.18 $0 +$33.88 $2247.70 16 $44.95 $0 +$33.72 $2236.46 17 $44.73 $0 +$33.55 $2225.28 18 $44.51 $0 +$33.38 $2214.15 19 $44.28 $0 +$33.21 $2203.08 20 $44.06 $0 +$33.05 $2192.06 21 $43.84 $0 +$32.88 $2181.10 22 $43.62 $0 +$32.72 $2170.20 23 $43.40 $0 +$32.558 $2159.35 24 $43.19 $0 +$32.39 $2148.55
Credit Card Table Reflection Questions Sample Student Response Using your Credit Card Table, answer the following questions: 1. How do the introductory interest rate and the APR affect your credit card balance? These amounts continually add to the total credit card balance, preventing a quick pay-off time. 2. What happens to your monthly payment throughout the first year? It decreases very slowly. 3. When do you think you will pay off your credit card? Ten to fifteen years 4. How would the payments, percentages, and balance be affected if you continued to make purchases with your credit card? It would cause the balance and payments would increase because of the percentage rate. 5. How would the fees change if you paid more than the minimum payment? The balance and fees would lower.