Can real interest rates be negative?

Recall that the real rate of interest, r, is the nominal rate of interest, minus the rate of inflation. If inflation suddenly increases, this will mean that the nominal rate of interest on many loan contracts will not cover the true opportunity cost of the money, and borrowers will repay those loans with money that is worth less than the money that they borrowed.

Consider an example, where you borrow $100 from me, for one year, at a nominal interest rate of 10%. Let's assume that we both expect inflation to be 5% during the year. My expected real rate of return or real rate of interest is 5% -- 10% - 5% for inflation.

You will repay me $110 at the end of the year. After a year, though, the value of my original $100 is now $105, as the result of inflation. So, my real return is not the full $10 of interest that you paid me; it's only $5, which is left after I account for the fact that $110 is worth less in a year because the currency is losing value.

Now, consider the same loan, where we both expect 5% inflation, but we are surprised to learn that actual inflation during the year is 20%. You still pay me $110 at the end of the year. However, the original $100 that I loaned to you is actually worth $120 at the end of the year, adjusting for inflation. I received $110, which is $10 less than the equivalent value of what I spent -- so I have a negative return or a negative real rate of interest.

You can see that I would not continue to lend you money at 10% interest. I would learn to expect higher inflation, and the nominal rate would rise. Thus, negative real interest rates generally do not persist for very long periods of time.