Is zakat obligatory on the balance available in a credit card and paid off monthly, and if the answer is yes, how is zakat calculated on the amount used?

First: A credit card free from Shariah prohibitions, such as usury (riba) or late payment penalties, is permissible.

Second: If the amount deposited in your account (e.g., 10,000) is available for withdrawal or purchase, it is considered your property and is subject to Zakat if a hawl (lunar year) passes while it is in your possession, even if the card involves usury (with repentance from usury). However, if the purpose is merely to allow borrowing for purchases without actual ownership of the amount, then no Zakat is due on it.

Third: If you borrow an amount and it remains with you until a hawl passes, it is subject to Zakat along with your other wealth. However, if you purchase goods with it for non-commercial purposes, there is no Zakat on those goods, and the debt is not deducted from your other wealth when calculating Zakat. The correct view is that debt does not prevent Zakat.