You are wrong about bank profits and interest rates traditionaly high interest rates have meant lower bank profits and low interest rates, higher profits.
Regardless of the level of interest rates the margin banks make remains faily constant, the competition between banks and non bank lenders sees to this. Lending for banks is a volume business the more loan business written the more profit. As interest rates increase the amount of new loans taken out decreases, that is the aim of increasing interest rates in the first place. As less loan business is written, there is lower volume which leads to lower profit.
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