What is the logic the Fed used for paying interest on reserves?
According to Bernanke himself, interest paid on reserves in excess of the penalty free upper bound are used as an additional tool with which the Fed can place a floor on the federal funds rate.The logic here is that banks have no incentive to lend in the overnight market at rates lower than this interest rate.

This link has some links to info on the topic. It's an old answer that got little attention and so here is my chance to get some use out of it :) 

Federal Reserve Interest