Summary: Banks charge for the ADMINISTRATION COSTS involved in the various services they perform. When they charge interest, that simply reflects the fact that they have to pay interest to their creditors (e.g. depositors).
Let’s assume a private bank sets up in a barter economy, and offers some wondrous new stuff called “money” which disposes of the inefficiencies of barter.
Citizens crowd into the bank, open accounts and offer collateral so as to enable their accounts to be credited. And let’s assume initially that citizens only want enough money for day to day transactions: i.e. no long term loans are involved.
Now clearly the bank will charge for administration costs (e.g. checking up on the value of collateral). But there is no reason for the bank to charge interest.
Interest is a charge made by a lender for the pain or inconvenience of foregoing consumption (i.e. saving) so that the borrower CAN CONSUME, or “spend”. And in creating money out of thin air in our hypothetical economy, the bank has not foregone consumption, so there is no reason to charge interest.
But of course that’s not to say that if you get a loan just to give you enough for day to day transactions from a bank in the UK in 2013 that you won’t be charged what the bank CALLS interest. The point is that if the bank does its costings properly (i.e. does not subsidise one type of customer paid for by excess charges on other customers) then the bank won’t charge you REAL INTEREST.
Long term loans.
Where money is created just for day to day spending, no long term loan is involved: the amount in each citizen’s bank account would bob up and down from one week to the next, but that’s it.
In contrast, there are long term loans. People don’t get loans just to sit a home admiring their newly acquired pile of money: they get loans in order to spend, i.e. consume the fruits of other peoples’ labour.
Now the only way to induce anyone to abstain from consumption is for the bank to offer interest to depositors. If interest is offered, then some people will leave more in their bank accounts than they otherwise would. And clearly the bank will have to pass that interest on to borrowers.
In short the bank won’t charge interest simply for creating money. But it WILL CHARGE long term borrowers interest, because for every £X of long term loan, there has to be someone making a long term deposit (or a series of people making longish term deposits).
Debt free versus debt encumbered money.
The above points have implications for the full reserve versus fractional reserve argument.
Checking up on the value of collateral involves a significant number of person hours, plus they aren’t cheap person hours: the people who do it are skilled. In contrast, the costs of producing central bank money in the form of physical cash is roughly 1% of face value. As to central bank digital money, that costs next to nothing to produce. So debt free digital money beats digital debt-money when it comes to cost of production. And that’s a point in favour of full reserve banking, though clearly there is much more to the full versus fractional reserve argument than the latter point.