Superlesson
Project 1-3

Advanced Algebra

Chapter 1, Mathematical Models

Credit card interest rates can be confusing. How can you find the best financial deals as you begin paying for your own purchases? Is credit a good way to pay for goods and services? Let's investigate using the Internet and mathematics!

Part A, Matrices and Data Handling

1. Different credit cards charge different rates of interest and annual fees. To help you decide which factors matter the most, look at the Credit Card page in the Financial Calculator site.

a. Set the annual fee = 0, and use the default amount for the rest of the values. These should be set to:

Amount Now Owed: $5000

Future Monthly Charges: $275

Future Monthly Payments: $350

Annual Rate: 17%

Hit the calculate button, then scroll down and look at the "Schedule of payments, etc." Write the first six months as a matrix, and label it Matrix A.

b. What is the dimension of Matrix A?

c. Change the interest rate to 6%. Now look at the "Schedule of payments, etc." Write the data for the first 6 months as a matrix and label it Matrix B.

d. What is the dimension of Matrix B?

e. Find Matrix A B. Explain what each column represents.

f. What is the dimension of Matrix A B?

g. Under the given circumstances, how much money do you save by paying an interest rate of 6% versus an interest rate of 17%?

h. Explain how you got your answer to a.

i. Notice that the dimensions of matrices A, B, and A-B are all the same. Must this always be the case to add or subtract matrices? Explain.

Part B, Multiplying Matrices

2. Suppose you make the following charges on your three credit cards over a two-month period:

Card 1 Card 2 Card 3

Month 1 $10 $32 $17

Month 2 $42 $8 $12

a. Write a matrix for the table.

b. What are the dimensions of the matrix?

c. For each card, you have to pay the amount of your purchase as well as any interest that has accrued. Suppose your monthly interest rates are as follows:

Principle Interest

Card 1 1 .01

Card 2 1 .015

Card 3 1 .005

d. Write a matrix for the table.

e. What do the numbers in the first column indicate?

f. What do the numbers in the second column represent?

g. What are the dimensions of the matrix?

h. Find the matrix product.

i. What do the numbers in the rows and columns of the matrix represent?

Part C, Making Connections

3. Notice that the dimensions of the matrices in parts a and d are different. Do the dimensions of two matrices have to be different in order to multiply them together? Either explain why they do, or give an example of two matrices that have the same dimensions but that can be multiplied.