Right now, interest rates can't go below zero, because if they did, people would just stuff the paper currency under their mattresses. But if there were no paper currency, if it was entirely electronic, then banks could charge negative interest rates.
"The trouble with paper money is that the rate of interest people earn on holding paper money puts a floor on the interest rate they are willing to accept in doing any other lending. For the US, I proposed making the electronic dollar the “unit of account” or economic yardstick for prices and other economic values, and having the Federal Reserve control the exchange rate between electronic dollars and paper dollars to make paper dollars gradually fall in value relative to electronic dollars during periods of time when the Fed wants room to make the interest rate negative."
--http://qz.com/29598/how-the-electronic-deutsche-mark-can-save-europe/
"So why can’t the Fed just lower the federal funds rate further? The
problem may surprise you: it is those green pieces of paper in your
wallet. Because they earn an interest rate of zero, no one is willing to
lend at an interest rate more than a hair below zero."
--http://qz.com/21797/the-case-for-electric-money-the-end-of-inflation-and-recessions-as-we-know-it/
To do this would require a new type of currency. Say goodbye to the greenback - its days are numbered.
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