No one can be screwed by a CC company if they pay their bill 100% on time every month.
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Never underestimate the pettiness of these people. More than once I have paid the full amount on a statement and then gotten billed for a few cents interest on the next statement without my making any other charges on the account. The first time this happened I simply paid the small amount and was astounded to get a bill for an even smaller amount the next month. When I finally called to ask the meaning of this insanity I was told that the first charge was for interest incurred between the time the bill was sent out and the time I paid it. The second charge for a few cents was said to be the interest incurred on the first miniscule amount after the bill was sent out. I simply told the person on the line that this could go on for eternity and I had no intention of paying two cents every month forever so they cancelled the remaining bill.
This has happened to me not once but at least three times! The only experience I can recall that was more frustrating was an account I set up at a hardware store for the little business I used to run. I mistakenly paid my bill twice which resulted in a credit balance. For the next few months I had little need for anything from the store and was amazed to find that they were charging interest on my credit balance! When I called about it they told me it was a flaw in their computer program and they would get it straight, nothing was done and I called a couple of more times and got the same story. Finally I called and really let them know I wasn’t going to put up with this and they corrected the balance and stopped charging interest. As soon as I needed something from them I used the credit and made sure I never had a credit balance again.