Yes but if I pay off the card every month then the bank is eating the cost of providing the credit. For example if I spend $500 over the month, by the time I get the statement and pay it by the due date I've probably had the use of the money - interest free - for lets say an average of 22 days. Additionally banks have to absorb the risk of deadbeat cardholders, etc. The card issuing bank also hast to pay visa/mastercard a fee every year. and finally the bank has to pays the company they outsource processing to (Total Systems/First Data/etc.). So the cost to the card issuing bank to provide credit is substantially greater than zero. In fact, if they are only making $100 in interchange fees they are probably losing money.

Also, I'm pretty sure the merchant bank gets a significant portion of the fee.