Explore credit card debt and installment loan terms in order to explain the mathematics that underlie the mathematical calculations and patterns of monthly finance charges, monthly balance on a credit card, and calculation of a fixed payment on an installment loan.

Part A

Think about something that you really want, but don't have the money for right now, and put the cost in the box under Month 1 and to the right of Avg Daily Balance.You decide you will not put any other purchases on the card.You still have a limited income so you are constrained to making the 2% minimum monthly payment with an interest rate (APR) of 21%.

1.What is the item that you put on your card? _____________________________

2.Use the table below to determine your monthly credit card balance for 5 months.

3.Show how you calculated each of the values for Month 1 by attaching a picture of your work.

Month 1

Month 2

Month 3

Month 4

Month 5

*Avg Daily Balance

**Mthly Finance Charge

Total

Min. Payment (2%)

New Balance

* Use your New Balance as the Avg Daily Balance for the next month.

** Monthly Finance Charge Formula (use 30 days for each billing cycle)

[(days in billing cycle/365) x interest rate] x Ave Daily Balance

Use an online credit card calculator (like https://www.bankrate.com/calculators/credit-cards/credit-card-payoff-calculator.aspx) to answer the following questions:

4.How long would it take you to pay off your credit card and how much will you pay in interest if you only made your minimum monthly payment?

Pay off time ______Amount of interest ______

5.The amount of interest incurred and the time to pay off the credit card is extremely high.What mathematical growth pattern or structure (linear, quadratic, exponential, etc.) leads to this high interest?

6.Explain how this growth pattern /structure leads to such high interest costs and payoff time.

7.If you paid an additional $50 a month to your credit card, how long will it take to pay off your credit card and how much will you pay in interest?

Pay off time ______Amount of interest ______

8.Explain why making a payment greater than the minimum payment significantly reduces the total interest paid and the length of time to pay off the credit card.Use data from your online calculator and your understanding of the mathematics to explain this.

9.Would it financially be more beneficial to lower your credit card interest rate to 15% or to make an additional $50 payment each month?Use mathematics to justify your answer.

10.Is there ever a time when you don't have to pay interest on a credit card? Eplain.

Part B

You have just decided to buy a used automobile, but will need to borrow $5000 from the bank to complete your purchase. You have already spoken with the bank loan officer about the terms of the loan. The terms are:$5000 loan made at a 10% rate of interest (APR), to be repaid in equal monthly installments over 3 years.

11.a. What is the value of the monthly fixed payment on your auto loan? Show all work on a piece of paper and take a picture.

________________________________________________

The monthly payment can be found by using the following formula:

Where:

P=Monthly Payment

Pv = Present Value (beginning value or amount of loan)

r =Interest rate (as a decimal)

n=# of interest periods for overall time period (i.e., interest periods per year * number of years)

Use an online installment loan payoff calculator to double check your calculations from question #8 and to answer the following questions:

b.How much will you pay in interest? ______________

12.a. If you paid an additional $50 a month to your auto loan, how long would it take you to pay it off? ___________

b. How much will you pay in interest? ______________

13.Why is it important to understand the underlying mathematics for computing credit card debt and installment loans?

Part C

14.Sometimes credit card debt can be referred to as a debt snowball, meaning that the debt keeps growing, out of control.If you keep using your card while only paying the minimum balance, explain why this would happen. Include mathematics in your answer. You may use the table below to help with your explanation.

Month 1

Month 2

Month 3

Month 4

Month 5

Balance at the beginning of month

0

New charges

Total

Min. Payment (2%)

New Balance

15.Reflect on this activity in a paragraph.Some questions to consider: Was there anything that surprised you?Are credit cards always bad? Would you ever use a credit card? Why or why not? Would you ever get a loan? Why or why not? What are the differences and similarities between credit cards and loans?