Higher interest rates are themselves higher costs. I think there’s more a symbiotic relationship between the two than a cause/effect one. If one raises, then you’ve affected the other. In our controlled economy, arbitrary decisions to increase interest rates are met by increased prices to confront increased costs.
I know for a fact because I lived through it, high inflation led directly higher rates on savings and CDs during the Jimmy Carter era. So that higher interest paid, led to higher interest rates across the board.
Ironically, during that stretch, my father in law pointed out that the “guaranteed” interest on his money, T bills, money markets was so high that it was not really worth the risk of his investments in his own business for the profits he was making. It was in reality, more profitable and much less risky to put his money into those things than to tie it up in accounts receivables that might not get paid.
His point? Look what it was doing to hinder genuine, protective business.