How/why do interest rates set by central banks affect market/retail interest rates?

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Aldric
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I understand that central banks ( the U.S. Federal Reserve and the Bank of England in the UK ) set their own interest rates for loans to / take deposits from government and commercial banks . MedlinePlus MedlinePlus I do not understand is how / why the rate set by the central bank affect the rates charged by my bank for loans and mortgages . Is not my bank is free to charge whatever they want , regardless of what the central bank charges ? MedlinePlus MedlinePlus I would have thought that competition between retail banks would be the main factor affecting interest rates . MedlinePlus MedlinePlus Maybe I'm being stupid ... Could an economics student , or other person in the know ' get well ?
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