A current account is a bit like a short-term bond. It is a valuable commodity that is created by banks and can be traded in the market. The difference is that bank trading systems allow current account balances to be used directly as payment, without having to be converted into cash first. Therefore the current accounts themselves are being used as payment, and count as money in their own right.

This is why current account balances are counted in all the official measures of money quantities, including the most strict measures such as M0.