Although the Federal Reserve does not directly control interest rates, its actions have an impact on the credit market and other financial markets.
The cost of funding for banks decreases when the Fed lowers its target range. Typically, they pass this savings on to customers by lowering the prime rate, which lowers loan and credit card interest rates.
Nearly every sector of the economy, including credit cards, is impacted by an increase in the federal interest rate. Every time the Fed decides to raise the federal benchmark interest rate, credit card APRs rise. If you have credit card debt, that can end up costing you more money in the long run.
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