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This is know as two-cycle billing and is widly used by the credit card industry.

What they do is average your balance over the last two months and charge you interest on that amount.

This means you pay more interest in the month after you get rid of a balance. It also means you pay less interest the first month you have put the balance on the card because they are averaging in the no-balance month before that. I think a lot of them start the two-cycle balance the second month you have the card, so they can still charge you on the full balance if you run it up right after you get it.

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