From my understanding it's tied to something called the 'prime rate', but what is that really and who determines what it is? Is it always less than the rate of inflation?
The prime rate is the interest rate banks use amongst themselves to lend money to each other only.
It is used as the basis (sometimes) for what interest rate banks charge you. The prime rate is based loosely on the Fed rate. There is a committee that meets regularly to set this and other industry interest rates.
I am not 100% positive the following is totally accurate
The banks keep our deposits and pay us interest for doing so. They are paying us interest because they take yours, mine and everybody elses deposits as a large lump sum and invest that money. Sometimes as business loans, sometimes as mortgages and sometimes as credit card.
The banks have a book of business that will be EXACTLY how much credit they have extended to everybody. But they do not keep that amount of cash in the vaults, only some smaller percentage of that large amount. When I use my credit card and they need to transfer money to amazon.com, if they don't happen to have enough cash that day, they will just borrow from another bank that does, and the interest rate they pay to do so is the prime rate. Since they are paying interest on the money they borrow to pay the debt I charged because they told me my credit was worth so much (...???...) they charge me a little bit more than that.
Hence your credit card or mortgage's APR being based on the prime rate.
I THINK that is what they do If I am wrong leave a comment and I will update, or the mods can.