Chapter 4.CR, Problem 12CR

Reminder Round all answers to two decimal places unless otherwise indicated.

Credit Card Payments You make one charge to a new credit card, but then charge nothing else and make the minimum payment each month. You can't find all of your statements, but the accompanying table shows, for those that you do have, your balance $B$ in dollars, after you made n payments.

Payment n	$2$	$4$	$7$	$11$
Balance B	$478.73$	$440.74$	$389.33$	$329.99$

a. Use regression to find an exponential for the data in the table. (Round the decay factor to four decimal places.)

b. What was your initial charge?

c. For such a payment scheme, the decay factor equals $\left(1+r\right)\left(1-m\right)$. Here $r$ is the monthly finance charge as a decimal, and m is the minimum payment as a percentage of the new balance when expressed as a decimal. Assume that your minimum payment is 5%, so $m=\mathrm{0.05.}$ Use the decay factor in your model to determine your monthly finance charge.