re: Will canceling an Amex card hurt my credit?

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With that in mind, these are both charge cards with no pre set limits. I haven't ever carried a balance on the gold card because the full payment is due at the end of each month per the terms of a charge card.

Will they take some sort of rolling monthly average balance to decide the credit they extended to me to calculate in with total credit utilization?

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The way they determine it is simply when the credit card company submits your information to the credit bureau. They pull it out in the middle of the month, if you owe 3,000 and have 5,000 limit it will show that, regardless of whether or not you pay it off in full every month. To the bureaus it is still perceived as a risk that you are charging up that much against your line of credit in one month. They won't know that you pay it off in full necessarily because it all depends on when the credit card company submits your information.