Negative rates do indeed exist in the real world. Central banks, for example, have set their very short-term rates negative to deter savings (depositor pays bank to save rather than the bank paying the depositor) and encourage credit growth and reduce longer-term rates (lending or investing in longer-term instruments). Of course, you won't get a negative-rate mortgage, this scheme is focused on money-center banks, not retail consumers. In other places like the commodity markets, you can also see negatives for things you might not expect. Oil prices were driven negative for a short time when there was no excess shipping capacity and the cost of shipping hyperinflated.