This makes no sense. If the bank lends $100 each to two people, it has to be prepared for them to take that money and spend it more or less immediately - on a house, or payroll, or whatever. When you put your $100 into the ATM, and two people get $100 bills from the ATM, where does the second bill come from?
The bank lends an amount at 7%. The individual immediately pays the full amount into someone else's bank account. If the bank needs cash (which it probably doesn't on a day to day basis because most of its depositors leave money where it is) it can borrow that amount from the other bank at 5.5% and profit from the margin. So the amounts are eventually consistent.
That's the basic logic: modern banking adds in a central bank that guarantees that it will lend enough to solvent banks at 5.5% to meet their customers' withdrawal requirements even if everyone pulls money out, banks treating each others' credit as equivalent in value to cash because they can always convert it, and a bunch of rules about lending needing to be banked with bank capital and other weighted assets to keep lending growth from being silly.
That's not how the banking system works in theory or practice. It hasn't worked like that for a very very long time.
Lending isn't limited by deposits, it's limited by central bank regulations.
Here's what the Bank of England says [0]
> if you borrow £100 from the bank, and it credits your account with the amount, ‘new money’ has been created. It didn’t exist until it was credited to your account.
> Regulation limits how much money banks can create.
Banks only need to maintain enough deposits to cover their liquidity needs - what they need to pay people withdrawing cash and what they need to transfer to other banks due to electronic money moving.
> it has to be prepared for them to take that money and spend it more or less immediately
Right, but the bank also knows that people are doing the exact same thing with other banks; borrowing money from the other bank which will get spent immediately back at this one.
Banks are prepared to meet the difference in money in and money out, they're not prepared to meet the total volume of deposits. When the bank gets this wrong there's a liquidity crisis (or a bank run) which causes Big Problems.
