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Image credit: iStock/Thinkstock.

Bank of America's (NYSE:BAC) shares took a drubbing this week after Federal Reserve Chairwoman Janet Yellen intimated that the central bank is "taking a look" at negative interest rates, and "wouldn't take those off the table."

Negative interest rates seem complicated, but they're easy to understand. Every bank has to keep 10% or so of its customers' deposits in reserve to pay funds out when depositors ask for them. Banks deposit these reserves at the 12 Federal Reserve branches -- thus the name Federal Reserve.

Banks earn interest on their reserves just like you and I earn interest on our deposits. The Fed currently pays an interest rate of 0.50% on excess reserves. This adds up quickly for the nation's biggest banks. JPMorgan Chase has $337 billion on reserve at the central bank, which will yield $1.7 billion in interest in 2016. Bank of America has $123 billion, which should earn $613 million in interest income this year.

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Data source: FDIC's Statistics on Depository Institutions.

This is where negative interest rates come into play. Negative rates mean that the Fed will start charging banks to hold their reserves. Thus, rather than paying banks 0.50% in interest on those funds, they'll instead charge them 0.25% (or whatever) to hold them. This would incentivize the nation's banks to put their $2.3 trillion in excess reserves -- that is, above and beyond what they're legally obligated to have on deposit at the Fed -- to work by lending the money out to businesses and consumers.

The logic behind negative interest rates is compelling. In Bank of America's case, a swing in rates from a positive 0.50% to a negative 0.25% would cost it $920 million in annual pre-tax income. That's a lot for a bank that earned only $15.9 billion last year -- and, mind you, 2015 was its best year in nearly a decade. To offset this, Bank of America would likely take its excess reserves and invest them in government bonds, or highly rated commercial paper, or by increasing its loan book. While this would presumably spur economic output, the downside to doing so is that it entails more risk. Even highly rated corporations and the most creditworthy borrowers default on their financial obligations from time to time.

Negative interest rates would thus lodge Bank of America, and all other banks, between a rock and a hard place. It couldn't leave the money on reserve at the Fed without impairing its short-term profitability. But by investing the funds elsewhere, Bank of America would add credit risk to its balance sheet, which could weigh on its long-term profitability. It's this catch-22 that caused Bank of America's shares to fall so precipitously on Thursday.

John Maxfield owns shares of Bank of America. The Motley Fool recommends Bank of America. Try any of our Foolish newsletter services free for 30 days. We Fools may not all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors. The Motley Fool has a disclosure policy.