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Hey there! I just did the same thing though in a more roundabout day (replied to an offer for 50k points and then had my best friend send me his referral code)---customer service made an exception and changed me to rose gold and kept me eligible for the 50k points--but again that was an offer.
If you dont' recall which offer you responded to--it's best to assume it was the public one--which is 35k points for spending 2000 in the first 3 months. If it was your first Amex, that is most likely what it was but you can also call and ask. Also, your credit has nothing to do with your offers, it's whether or not you've had the same offer before or "how many accounts you have opened and closed with Amex in your lifetime.."
Green/GOLD/Platinum = Charge cards... they don't get a CLI sicne they have no CL
Charge Cards = report as "OTHER" on your CR and don't factor into UTIL since there's no ratio to calculate as there is no CL
You have to spend $XXXX to get the 40K points. If it's 40K points it's a Referral link and not the public or incognito offer (50K)
If you want to confirm your offer you simply login, chat w/ Amex and they'll confirm the details of your specific offer and the requirements to get paid out.
You use it, you pay it, there's no interest charged unless you don't pay it by the due date. There's also a feature called POT - Pay Over Time where if you sign up for it you can move charges over $100 to it for a FEE and pay it like you would a CC instead of a Charge Card.
I suggest reading up the Amex threads before you venture further into Amex Land
You won't see your sign up bonus until you hit the spend and then it will show up pretty immediate, within a few minutes in some cases. You can always chat with them or call and they can tell you which bonus you applied under. They will have it listed a under a program number on their end which correlates to the correct sub.
Did you do any research about the card before you applied? Just wondering...