In the UK, the Bank of England has them set @ 0.5% and I know this is to stimulate the economy because we are in a deflationary period. I know that the banks savings rates change in accordance to the bank of England's rates but they are not exactly the same (i.e. 0.5%). Why do they offer customers larger interest rates? Sorry, to paint a complete theoretical picture of the business world is difficult for me.
How do interest rates relate to savings rates?
Banks need money to loan, so they offer larger APR to entice people to open accounts and save. When money is scarce (inflation - means it cost more to buy the same) rates usually rise, to lure more savers.
