Banks borrow money (your savings and deposits) and then loan money (home/business loans). The interest rate on the money they loan out (home loans) must be larger than the interest rate they pay out on the money they borrow (savings & deposits).
The central bank a.k.a federal reserve is another large pool of money that banks can borrow from. If the central banks increase their interest rates, in other words the fed increasing rates to fight inflation, then the banks must pay a higher interest rate for borrowing from the central bank. This means for a bank to stay afloat, they must also increase the interest rates on the loans they give out.
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