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If inflation outpaces the interest rates on a loan (as has happened on my mortgage) then the bank will end up with less purchasing power than it started with.
But is that really the case? From what I understand it creates the money to be loaned out of thin air through fractional reserve banking. They don't lend from their reserves or deposits. They gain the interest and lose nothing, because it's not their own money that's being inflated away. But since the loans need to meet the fractional reserve requirements, one could view loans at rates below the rate of inflation as an opportunity cost.
In the US, there are no reserve requirements on lending and there haven't been for several years, so clearly there's some other constraint. If banks could just spend arbitrarily out of thin air, why wouldn't each bank just buy every real asset in the world?
When the bank lends out money at a particular interest rate, it still needs the interest payments to cover its operating expenses. If inflation is outpacing the interest rates, then the bank will be operating at a loss.
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