Hey guys, first off I'm really new here and I wanted to thank everyone before hand for any help that is offered. Okay, I was given this problem in my pre-calc class as an extra credit 'research' problem. We are not allowed to ask our professor for help as it's extra credit and it was given to us with the intention of having us seek outside help. Here is the problem that was given, it's long and kinda complex:

Original Problem:

"In years past, the minimum monthly payment on a credit card has been calculated by taking 2% of the credit card balance. The only exceptions to this rule was a minimum the company would bill, we’ll use $5, unless the balance is less than $2, at which point the company would bill the balance. So, if you owed $1,000.00 at the end of a month your minimum payment would be $20; if you owed only $30 your payment would be $5; and if you
owed $0.52 you bill would be $0.52. Remember, no interest is charged on the first month!"

"A good interest rate for a first time credit card would be 18.99%, we will use that as our interest rate. We will assume that the interest is compounded monthly and that there is always the same number of days in each month."

"You are going to suppose you purchased a 32-inch flat panel television
for $999.99 (plus 7.75% tax and $8 Electronic Waste Recycling Fee) on
your credit card and pay only the minimum payment until the TV is
paid off. (not using the card for any other purchases) How long will it
take to pay off the TV and how much would you end up paying for the
TV in the end?"

"To help encourage Americans to pay off their debts faster, new law requires credit card companies to charge 4% minimum payments. Find the results of the above using the new 4% law. What is the difference?"

-End of problem.

Okay, I wanted to gett some help on the following:

1) First, how should I approach this problem?

2) Second, I'm really confused on a certain part of this problem - calculating the minimum payment at which point they charge a flat fee of $5.00 for. Let me elaborate:

X = total balance.

If X < $2.00 then the total balance get's billed as a minimum payment. Example - balance = $1.50, minimum payment = $1.50.

If X > $2.00 then a flat fee of $5.00 is issued as the minimum payment but I don't know where it stops giving $5.00 as a minimum payment then switches to taking 2% of the total balance?

If anyone here at all can help I'd really appreciate it. Much thanks to you guys who took the time to read this whole problem and my questions, I know it's very long and somewhat complex (at least to me).

Thanks again,