In Connecticut you would need to have a written agreement signed by your client or a statute that would permit you to charge interest or late fees for delinquent client payments. On consumer debts Connecticut's law of usury applies, and limits the amount. Commercial debts are subject to a different limitation.

With respect to credit cards...I think you will find in the fine print of the agreement that you agree to the various charges. At the time you receive an application there are usually disclosures as to the interest and fees applicable at the time.