CCNI1
How many in the class have a credit card? More than one? How old were you when you got your first credit card?
What do you use them for? Why do we like credit cards so much?
CCNI2
Instructor Notes
This young woman discusses how she lives more frugally after college than during her college years, even though she has a job, because of her credit card debt. She cannot afford a car payment because she has to pay off credit cards.
What are students' general impressions of this woman? Is she particularly irresponsible? Or is she basically normal? The statistics indicate that she is fairly normal.
CCNI3
Instructor Notes
Spreadsheets
Getting used to spreadsheets is a worthwhile goal in and of itself and a life skill students are likely to use later. The spreadsheet (or online calculators) will be used to explore the discussion questions on the next page.
Tie the discussion to other math courses.
Invite students to comment on the total amount of money paid and how this compares across interest rates.
This young man has over $140,000 in college loans and an additional $15,000 in credit card debt. How does this happen?
What were his assumptions about his ability to pay these off? What do you suppose were the assumptions his creditors made when they loaned him $140,000 for school?
CCNI4Instructor Notes
What do the students think would be a “wise” use of credit cards, or credit in general?
CCNI5
Instructor Notes
The next few slides are intentionally vague. When consumers make a decision about whether to take an offer like the one described here, the terms of the offer usually are somewhat vague and the decision is made at the register. In this module students can make an intuitive decision in discussions, but investigate the real consequences in the mathematical exploration.
This might be a good place to mention credit worthiness and credit ratings. Students may be surprised to discover that not everyone receives the same offer!
CCNI6
Instructor Notes
This page is a springboard for student discussion. In particular, the instructor might:
- Use it as an opportunity to define or review terms: balance, principal, interest, APR.
- Allow students to offer opinions and suggestions as to what would make the Target offer a good deal. These could be recorded and kept as a basis for reference, further discussion later, or extended inquiries.
The main conclusion of any discussion at this point should be that it is impossible to answer the question without doing some mathematics.
The penalties have huge consequences. Ask students to assess the probability that they will make a late payment. Why would someone get a returned payment? Do they think the penalty APR and fees are fair?
CCNI7
Instructor Notes
Use the sales tax for your state. Use 17.25% APR now for calculations. Later your students can look at the other two possibilities.
CCNI8
Instructor Notes
- Individuals or groups could be assigned different interest rates so that the results could be compared later.
- The formulas that students need to use to calculate the new balance and total payment should be reasoned out preferably by the students themselves in groups. Writing the formula in algebraic notation provides an important link to the algebra courses students are often required to take.
- Here is an example of a worksheet for 10% APR, no sales tax and a $50 monthly payment:
Month Balance Interest Payment New Balance Total Payment 1 900 50 850 50 2 850 8.50 50 808.50 100 3 808.50 8.09 50 766.59 150 4 766.59 7.67 50 724.26 200 5 724.26 7.24 50 681.50 250
Here is an opportunity for your students to set up a simple spreadsheet. They are going to have to use a calculator anyway, so you might as well encourage them to use a spreadsheet and experiment on their own. Then when they see the spreadsheet on slide 10 they will be suitably impressed!
CCNI9
Instructor Notes
This discussion refers to the worksheet offered in slide 8.
CCNI10
Instructor Notes
Spreadsheets
Getting used to spreadsheets is a worthwhile goal in and of itself and a life skill students are likely to use later. The spreadsheet (or online calculators) will be used to explore the discussion questions on the next page.
Tie the discussion to other math courses.
Invite students to comment on the total amount of money paid and how this compares across interest rates. Have them think about the shape of the graph produced by the spreadsheet (or some of the online calculators). Do they recognize the shape? This is an opportunity to discuss functions they have seen before.
The online calculators don't give all the answers that the spreadsheet does. But students can be challenged to figure out the answers using arithmetic.
For the future teacher.
In courses whose enrollment is primarily future teachers this module can open a discussion of number size and the mental number line (Siegler et al, [1]). What is a big number? Is a $1000 a lot of money or a little? How about the interest, does it feel like a lot or a little? Children carry a mental number line that is more or less logarithmically scaled. To a small child, 10,000 and 100,000 seem much closer in size than 10 and 100. Where the compression of scale begins depends on the stage of development.
Perhaps this is why, for adults borrowing money, if $100,000 seems like a huge amount of money then $200,000 doesn't feel that much bigger.
[1] Siegler, R. S. & Opfer, J. 2003. The development of numerical estimation: Evidence for multiple representations of numerical quantity. Psychological Science, 14, 237-243.
CCNI11
Instructor Notes
Students should see by the end of this discussion that, although more than one payment plan may save them money, they gain the most advantage by paying the loan off sooner. Later they will look at the effect of different interest rates on this calculation.
CCNI12
Instructor Notes
Reality
No credit card company lets you do either of these things any more, do they? Why not? This could spark an interesting class discussion of both the mathematical nature of debt and the ethical questions of who should bear the responsibility for the propensity of consumers to get themselves into trouble.
Tie the discussion to other math courses.
This page is intended as a possible link to college math. In the case where the consumer makes no payments, what is owed every month increases. There is an easy way to compute the total owed using a hand calculator. Just take the principal and multiply it by (1 + monthly interest as a percent) for as many months as you want. Each multiplication gives the new amount owed. Students can generate a graph from this data (or use the spreadsheet with zero payments to see the graph). The interest then becomes a relative growth rate, giving the percentage by which the balance grows every month.
What is the formula for this calculation? A similar question could be asked about the case of linear growth.
CCNI13
Instructor Notes
Writing
These explorations offer the possibility of writing assignments where students must support their arguments with calculations and graphical displays. Figures should be used as a basis for argument and not just placed in the paper like ice cubes in a punch bowl. Here are some possible topics:
- Suppose the minimum payment is $40. When is it safe to buy $40 of merchandise each month? Write an explanation and support it with calculated examples and graphs. The point here is that it is always “safe” to pay off the balance every month, but if you have a standing balance before you spend the $40, you have to keep paying interest on it.
- What kinds of purchases might lead to a regular monthly charge to your credit card? Have students give some examples such as cell phone bills, etc.
- What happens if you pay the minimum balance of $40 every month, but pay it late? Recall that there are penalty fees on this card for late payments.
- What is the difference between an extra payment of $100 in the first few months versus a payment of $100 made a year later (at 13 months) in the total amount you have to pay for the computer?
CCNI14
Instructor Notes
At this point the class may be ready for a more complex situation. Here is a link that allows you to download a file containing several credit card offers that students can study to extend their understanding.
Here are some activities you might do with these offers in your class.
Comparing offers
Consider several student credit card options. Provide students with the details for the credit card offer. Ask them which would be the best offer for them. They will likely have no idea. Hopefully they will ask about APR for payments, APR for transfers, APR for cash advances, minimum interest charge, Annual Fee, Transaction Fee, Penalty Fee etc. These can lead to a discussion about what these terms mean.
The class could then choose a scenario and track monthly payments that would trigger various fees. Students would then be given three different credit card options.
- High interest no annual fee,
- low interest with an annual fee,
- high interest with an annual fee.
There will be pros and cons to the first two options. The students should hopefully recognize that the third option is a bad deal.
Reading the fine print
Look at the two specific cases of Cash advances and missed payment. Have students work in two groups examining one of the two topics in a fashion similar to the last exercise. When they get a handle on their understanding they can then present their findings to the class or write a short paper.
CCNI15
Instructor Notes
We suggest a writing assignment to conclude this lesson. Here are two possibilities:
- The Hands on Banking: Young Adults
Instructor Guide contains tips for credit card use in "Topic 5 - All About Credit page 47
'Killer credit card tips!'".
How many of the tips did you have on your list?
Did you have a tip not on the list?
Is there something on the list that you still do not understand? - You have been hired to write an explanation of credit cards to students your age. In your own words what would you tell them about the pros and cons of credit cards. Be sure to explain financial terms in your own words, support your claims with calculations, graphs or other mathematical evidence, and give examples that could really happen to you.