Credit card interest rates are important, especially when you're the type of cardholder to carry your credit card balances rather than pay them in full each month. Your credit card issuer can increase your interest rate, usually "any time for any reason" if your card agreement allows for universal default. Read 16 Explanations for Interest Rate Increases for a list of reasons that credit card issuers commonly increase interest rates.
FDIC Consumer Protection laws mandate banks to give 15 days notice before a change to the credit card agreement can go into effect. This include interest rate increases. So, your credit card issuer must let you know your interest rate will be increasing at least 15 days before it actually increases. During this 15-day window, you'll have the opportunity to opt-out of the changes if you don't accept them. If you choose to opt-out, the creditor will likely close your account, but allow you to repay the balance at the lower interest rate.
Credit card issuers don't always have to notify you before increasing your interest rate. If the rate increase is due to a "delinquency or default" on your part, the creditor doesn't have to let you know the rate will be increasing. Typically, these types of penalty increases are outlined in your credit card agreement. For example, if you make a late payment, even on another credit card, your creditor could increase your interest rate without letting you know in advance or giving you a chance to opt-out.

