During the last few years, the Fed has been paying banks interest on reserves. Its a strange policy if you want banks to invest their money in the real economy. Why did they do this? Is it a way to recapitalize the banks? Is it a way to guarantee their solvency irrespective of the availability of investment opportunities? Is it a way to limit the potential inflation of QE?
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 :)
The aim of this policy (introduced in 2008) was to "give the Fed better control of the short-term interest rate" via reducing the demand for short-term government bonds by taking out some of the excess cash that banks hold.
In a crisis, banks are not lending, and thus the cash they have is poured into many assets, including short term government bonds. This reduces the market short-term nominal interest rate. To control for this, the Fed has to sell some of their T-Bill holdings in order to reduce the money supply. Yet, the intervention of the Fed are more precise if the amount of cash willing to participate in that market is smaller. That is why offering banks an incentive to gain a return by parking part of that cash into US regional Central Banks helps to lower that demand.
Certainly, this policy also helped banks to build up their assets. However this has been a relatively very minor issue, according to a recent inlet in The Economist (March 18th). The graph is below:
There is some opposition to this policy though. On the one hand, some say it reduces bank lending. On the other hand, as the graph show, the official forecast for the interest paid on these reserves is likely to increase considerably in the coming years, mainly because the Fed is now increasing the interest rate. Politically, this is a hard-seller, albeit Trump might not be very worried about this. Who knows.