What are you asking? Central banks generally do various things, like controlling the money supply and bailing out other banks if they get in trouble in a way which is going to damage the economy. Obviously there wouldnt be a government mandated central bank if you had anarchy, but there could still be a de facto bank which acted as the centre if the private banks thought this would be a useful thing to have.
http://www.federalreserve.gov/moneta...scountrate.htm = base interest rate