In my macroeconomics class, our professor showed an example of the introduction of the credit card. She says that this will decrease the money people are willing to hold, and thus increase the money velocity. But why is that true? I mean, although it seems like the credit card as a new mean of payment makes us feel we are not holding much money, but the credit card company are actually paying for us them using deposits. So the money people hold didn't actually change because while consumers hold less cash or deposit, banks that offer credit card will need to hold more cash or deposit to pay for it. So I think the claim that money velocity increases is false. Am I right?
Credit cards are a way of deferring payment in the form of inter-temporal substitution; it helps reduce the household's liquidity constraint that may prevent it from consumption smoothing as much as they would like if their transitory income was much more spread over the household's lifetime.
You are right that the amount of money doesn't change. Loans require giving away money, but credit cards are a way of creating debt, so banks do not need to hold more cash to give a line of credit like you suggest.