## The Cost of Being Late

- Lesson

We are bombarded in the media with ads offering 0% interest or teaser rates of 2.9%. These ads are devised to entice us to sign up for these limited time offers that the companies tell us would be crazy to miss. The goal of these ads is to get us to use credit to buy on impulse. If we take the time to analyze the offer, we might realize that if it sounds too good to be true, then it probably is. In this lesson, students will work through a credit card scenario with a teaser rate, minimum payments, fees, and rate increases for being late.

Getting your first credit card can be very exciting, but unfortunately some people do not take the time to consider the costs associated with buying on credit. A credit card can make it easier to buy on impulse, and we do not always take the time to consider the hidden costs of buying on credit. This lesson will help kids understand the perils of making impulse purchases on credit, paying only the minimum each month, and/or making late payments.

In this lesson, students will work individually or with a partner to answer a series of questions related to buying on credit. They will first work under the assumption that they are not paying off the balance but will make the minimum payment and revolve the debt. Once they have seem how much the cost of borrowing on credit and making minimum payments effects their overall cost of the items purchased on credit, they will rework the scenario to formulate an optimal payment plan for paying off the debt within a time from of six to twelve months.

There are two options for working through this lesson. Option one is to use the Compound Interest Simulator and the second option is to use the Cost of Being Late Spreadsheet to compute the interest each month.

Cost of Being Late Spreadsheet

Regardless of the method chosen, you may want to walk through some practice scenarios to ensure your students have a working understanding of how interest is calculated. An alternative approach would be to divide the class in two and have one half of the students use the simulator and the other half a spreadsheet. As part of your post activity discussion you can have students discuss the benefits of one method over the other.

The primary goal of this lesson is to understand that the costs associated with buying on credit and that making only minimum payments is problematic to long-term financial health. The secondary goal is to formulate a plan to extinguish the debt quicker. This lesson will help them see the real cost of purchasing an item when interest and fees are added to the purchase price. The scenario that will be used for this lesson is based on the first year of the life of a new credit card. The student handout describes the scenario and posses a series of questions based on the use of either the simulator or the spreadsheet application.

### Lesson Opener

In order to assess the level of consumer finance knowledge your students posses, consider asking students to discuss the following questions in small groups or as a whole class:

- What does it mean to purchase something on credit?
[Answers will vary, but what you are looking for is to see if students know that interest and/or fees can be associated with purchasing on credit. Help them understand that unless a credit purchase is paid in full on or before the due date that the credit granter will charge them interest (rent for the use of the credit grantors money).]

Show students some ads that depict unrealistic interest rates or zero interest for extended periods of time. Car ads are a great visual tool since they often times advertise unrealistic rates over long periods of time.

- How can a merchant stay in business if they are lending
money to consumers to purchase goods but not charging interest for the
use of that money over time?
[Answers will vary from students not having any idea to other students surmising that the price of the merchandise is higher to reflect the cost of borrowing. This is correct and often times in the fine print of the add there will be a disclosure indicating a discount for cash purchases.]

- What is the difference between simple interest and compound interest? Which do credit card issuers use?
[Simple interest is the amount of interest based only on the principal amount owed. Compound interest is interest calculated on the sum of the principal and any previous interest. Credit card issuers typically use compound interest. How exactly interest is calculated will vary with credit card issuers. For more detail on how interest is calculated, see the disclosure statements provided by various issuers.

*Note: The reading level of most credit disclosure statements is beyond the comprehension of most middle school students.*] - What is meant by minimum payment and who determines the minimum?
[Some students will be under the impression that they can determine how much they want to pay. This is not necessarily true. The minimum payment is usually a percentage of the outstanding balance or a flat rate that must be paid on or before a specified date. In 2005, the minimum payment was changed from 2% to 4%]

As a whole class, ask students to share what they knew about credit cards. Expect that they may share family experience or repeat what they have heard in the media. If it does not come out in the class discussion, make sure students understand that the use of a credit card creates debt and a legal obligation to pay while a debit card takes money from an existing checking or savings account to pay for purchases and does not result in a debt obligation. The terms debit card and credit card are often times mixed up by students and even some adults. If you have not already done so, this would also be a good time to share some the ads offering teaser rates or extended payment options. Be sure to point out the fine print that is usually at the bottom of these ads. The fine print will often disclose the true cost of credit based on a simple scenario.

The scenario we will use for this activity includes the charging of three retail purchases and a dinner for friends. Distribute either the Cost of Being Late: Compound Interest Simulator or Cost of Being Late: Spreadsheet Application Activity Sheet, depending on which method students will use.

Cost of Being Late: Compound Interest Simulator Activity Sheet

Cost of Being Late: Spreadsheet Application Activity Sheet

For simplicity, no additional charges will be made over the next twelve months. The scenario will be based on a teaser rate of 10% for six months and a default rate of 22% thereafter. (The default rate is the published rate without benefit of any promotional offers. It is sometimes referred to as the posted rate.) One payment will be made late resulting in a late fee of $40 plus an increase in the APR from 22% to 28%. Our goal will be to determine the balance due at the end of one year along with the cost of using credit for that twelve-month period. If your students are struggling with the concept of compound interest you may want to consider having them work with a partner pairing a weaker student with a stronger student.

### Compound Interest Simulator Option

Before you have the students begin work on the scenario you might want to walk through an example using the simulator. I would recommend using the following mp3 purchase as an example.

Have students consider the purchase of an mp3 player at a cost
of $200 with payments of $20 per month and an interest rate of 22% APR.
Have students enter the information into the simulator as follows (**Note:**
Only whole numbers can be entered into the dollar fields, which means
kids will need to round up or down using standard rounding rules):

It will take twelve months to pay for the player for a true cost of $222.98. That true cost will be even higher if payments are not made on time and late charges are assessed or if interest rates are increased before the debt is paid in full. In this example the cost of buying the player on credit was $22.98. Consider asking students what they could have done with that $22.98 if they had not bought the player on credit and instead waited to pay cash.

A minimum payment of 4% or $20, which ever is greater is standard but since it is an open field you can have the kids work with a variety of scenarios. You might consider having them see how long it will take to pay off if they make minimum payments of $10 or if the rate were higher or lower. Depending on the skill level of your students and time constraints you might ask the students to pose an additional example that they could use the calculator for such as a new game system or some other consumer purchase that may be of interest to them. Some students may want to simulate the purchase of a car which can be done but I would recommend using the purchase of a big ticket item such as a car as an extension activity.

Your students should now be ready to work through the scenario using the Compound Interest Simulator. I would recommend that you walk around and spot check student’s work to insure their calculations are correct and that they understand how to use the simulator.

### Spreadsheet Application Option

In option two instead of using the simulator use the Cost of Being Late Spreadsheet. The application provided with this activity has the formulas built in and is based on a twelve month scenario using the mp3 example described in Option 1.

Retail Credit Card Purchase of an mp3 Player Example | ||||||

Payment # | Initial Balance | Purchases | Fees | Monthly Payment | Annual Interest Rate | Interest Charges |

– | $200.00 | – | 22% | $3.67 | ||

1 | $203.67 | – | – | $20.00 | 22% | $3.37 |

2 | $187.03 | – | – | $20.00 | 22% | $3.06 |

3 | $170.10 | – | – | $20.00 | 22% | $2.75 |

4 | $152.85 | – | – | $20.00 | 22% | $2.44 |

5 | $135.28 | – | – | $20.00 | 22% | $2.11 |

6 | $117.40 | – | – | $20.00 | 22% | $1.79 |

7 | $99.18 | – | – | $20.00 | 22% | $1.45 |

8 | $80.63 | – | – | $20.00 | 22% | $1.11 |

9 | $61.75 | – | – | $20.00 | 22% | $0.77 |

10 | $42.51 | – | – | $20.00 | 22% | $0.41 |

11 | $22.92 | – | – | $20.00 | 22% | $0.05 |

12 | $2.98 | – | – | $2.98 | 22% | $0.00 |

Totals | – | $222.98 | $22.98 |

The benefits of using a spreadsheet over the simulator are that the spreadsheet provides a monthly amortization (payment plan) where the simulator does not. If time permits, you may consider having students use both methods.

### Answers

Simulator | Spreadsheet | |

1. | $532.00 | $532.00 |

2. | $516.43 | $516.43 |

3. | $436.63 | $436.63 |

4. | $419.43 | $419.11 |

5. | $128.21 | $127.11 |

Note: Some values differ because the Compound Interest Simulator only accepts input values in whole dollar amounts.

- Copies of print ads promoting low or no interest on the purchase of goods or the use of credit such as:
- 0% APR for 72 months
- 2.9% APR for 60 months
- Zero down and 0% interest for 12 months

- Computer with Internet connection or spreadsheet application
- Chart paper and markers (optional for presentations)
- Cost of Being Late Spreadsheet
- Cost of Being Late Activity Sheet: Compound Interest Simulator version or Spreadsheet Application version

**Assessment Options**

- Collect the activity sheets and check for completeness.
- Have students do presentations of their overall findings.
- Modify some of the parameters of the activity, such as initial spending and missed payments, and have students redo the activity.
- Ask students to simulate the worst case scenario where no payments are made and calculate how much is owed after a year.
- Have students collect data on their own spending and pretend they paid it all with a credit card, then calculate the cost as they did in the activity assuming they made only the minimum payment every month.

**Extensions**

- Invite an issuer of credit cards to come in and talk about the process of apply for and gaining approval for a credit card.
- Have students collect disclosure statements from various credit card issuers to determine how they calculate the balance from which interest will be calculated. This extension is only recommended for teachers who are comfortable with consumer finance and disclosure statements as it can raise many questions that could prove difficult to answer. Also, the reading level of many disclosure statements is beyond that of the typical middle school student.
- Invite a consumer credit counselor to come in and share stories of people’s lives that were changed for the worse due to misuse of credit cards. This could be a panel consisting of a consumer credit counselor, bankruptcy attorney, and debt collectors.
- Alter the scenario to include additional purchases made in the first year, cash advances, and/or additional charges for late payments and being over the limit.
- Have students interview an adult who uses credit cards to determine what advice they would have for a person who had just received their first card.
- Have students’ research how a credit card issuer calculates
the interest due each month and what amount is used as the basis for
the calculation.
In its simplest form, credit card issuers take the outstanding principal balance plus any new charges and/or fees, less any payments or credits as of the statement cycle date then they calculate the interest due using the formula Interest = principal×rate×time. For example:

Outstanding principal balance = $340 New charges = + $75 Fees or previous months interest = + $10 Payments = – $25 Balance on cycle date = $400 Assume an annual percentage rate (APR of 12% or 0.12) Assume time of one month ( ^{1}/_{12})I = ($400)(0.12)( ^{1}/_{12}) ≈ $4The outstanding balance due is now $404. By repeating this process each month we are compounding interest. Interest rates are always quoted as annual percentage rate (APR). To determine the rate charged for one month you would need to divide the annual percentage rate by twelve. Some credit card issuers will use average balance or blending of average and actual balances to determine the basis for calculating interest. Methods can vary greatly between credit card issuers. This lesson has been simplified for the age level of the students. For more information on actual practices by credit card issuers see the Federal Reserve Board

**Questions for Students**

1. If the interest rate were cut in half, would the time to pay off the debit also be cut in half?

[Expect some students answer yes to this question. If they do, I would recommend projecting the simulator and entering a rate that of 11% for the mp3 player example. At 22% the balance due in the 10th month will be $22.51 while at 11% it will be $10.65. The overall cost of credit drops from $22.98 to $10.75, which is a change of $12.23 or 53%. You may want to ask students why the interest paid was cut by more than half when the interest rate was cut by exactly half. The answer is the interest was reduced by more than half because we did not change the minimum payment amount of $20 therefore more was applied to the balance with the lower rate.]

2. If we doubled our payment from $20 per month in the scenario to $40 per month, how long will it take to pay off the debit?

[If we leave in the late payment fee and increased interest rate then will will take approximately 16 months to pay the debt in full.]

3. Does interest added to your balance reduce your available credit line?

[Yes, your outstanding balance includes principal balance, interest, and fees. Your available credit is your credit limit less this balance. It is possible to incur an over limit charge if the applied interest puts you over your credit limit.]

4. Can you make more than the minimum payment?

[Yes, your payments must be equal to or greater than the minimum payment. You can pay off your balance ahead of time as well as make payments before the due date.]

5. Can you re-negotiate your interest rate?

[Yes, it is sometimes possible but these negotiations are handled by the lender on a case-by-case basis after taking into consideration the borrowers credit history.]

6. Why is it better to have a lower rate of interest?

[Answers may vary but what you are looking for is for students to recognize that if the rate is lower that more of their minimum payment will be applied to the outstanding balance. It also means that the cost of buying on credit is less. Buying on credit is like paying rent to use someone else’s money. The lower the rate (rent) the lower the cost is to borrow.]

**Teacher Reflection**

- Did students have the background knowledge necessary to complete this activity? If not, what changes would you make for the next time this activity is used?
- Was students’ level of enthusiasm/involvement high or low? Explain why.
- Did you challenge the achievers? How?
- How did the students demonstrate understanding of the materials presented?
- What were some of the ways that the students illustrated that they were actively engaged in the learning process?
- Did you find it necessary to make adjustments while teaching the lesson? If so, what adjustments, and were these adjustments effective?
- What worked with classroom behavior management? What didn't work? How would you change what didn’t work?

### Learning Objectives

Students will:

- Experience the impact to the overall cost of borrowing on credit when:
- Interest rates increase.
- Fees are assessed for late payments.
- Minimum payments are made.

- Modify the scenario to optimize payments for quicker repayment.
- Modify the scenario to determine the impact of multiple late payments.

### NCTM Standards and Expectations

- Work flexibly with fractions, decimals, and percents to solve problems.

### Common Core State Standards – Mathematics

Grade 7, Ratio & Proportion

- CCSS.Math.Content.7.RP.A.3

Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

Grade 7, The Number System

- CCSS.Math.Content.7.NS.A.3

Solve real-world and mathematical problems involving the four operations with rational numbers.

Grade 7, Expression/Equation

- CCSS.Math.Content.7.EE.B.3

Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.

### Common Core State Standards – Practice

- CCSS.Math.Practice.MP1

Make sense of problems and persevere in solving them.

- CCSS.Math.Practice.MP4

Model with mathematics.

- CCSS.Math.Practice.MP5

Use appropriate tools strategically.

- CCSS.Math.Practice.MP7

Look for and make use of structure.