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I'm not sure if anyone has experience with this, but I have an AMEX charge card that has a $2.4k past due balance (which was due last month), in addition to about $400 in charges that are due this month (so $2.8k total). I'm currently able to pay the $2.4k by the due date, but I'm not sure about the $400.
Will AMEX report the account as 30 days late if I pay off the current past due balance but miss the payment that's due for this statement (the $400)?
Yes.
No
The $400 is considered "current charges"
Edit: To be on the safe side, you can call Amex and ask them
Amex, at least for the charge cards, report to the bureaus when you are a consecutive 60 days late.
30 days late is reported when you're 30 days late. If the 2.4k was due 5/1, you have until end of tomorrow for it to post before it will be 30 days late. If the additional $400 is for a different statement, that's a different 30 day countdown. Like someone else said earlier, it's the internal system that will hurt you.

Well we'll agree to disagree. I had an account rep share the 60 day rule with me about 3 months ago and when i, for the first time ever, paid at the 37 days mark they did not report it. Maybe I was just lucky.
Oh and if you have excellent payment history with them but may a flub, you can ask them to remove their internal reporting of the last payment and internally 're-age' your account. This has no bearing on what gets reported to the credit bureau but rather what they see as your payment history within their internal systems.