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Say you use a $0 fee 4% APR credit card convenience check of $3000 for half a month. That's $10 in interest, but if it all happens within the same billing cycle, do you still pay that interest because there’s no grace period, and if so will it be posted on the statement date?
No, they don't have a grace period.
If there's no grace period, the interest will post once your new statement is generated. If you're concerned about your account posting a balance, then push a payment through your bank's bill pay service which includes the interest.