Negative interest rate

Sounds crazy I know

Why would anyone pay interest to someone they are lending money to ?

But it's not as crazy as it sounds if the lenses has another reason to lend.

For example if someone in an economy where there is high inflation, low nominal interest rates and also risk of an economic crisis may want a safe haven such as a Swiss bank and is prepared to pay the Swiss bank to keep their money safe.

Moreover a negative one percent interest in a bank in a country where inflation is very low , say 1percent means the real interest rate is minus 2 percent while in a country with higher inflation , say 3 percent and an interest rate of 0.5 percent actually has a real interest rate of minus 2.5 percent - which is a worse deal for the saver.

The Bank of England base rate is the interest paid to commercial banks on the reserves held by the Bank of England so that commercial banks can settle their accounts with each other. This is an important service and a legal requirement that commercial banks may be prepared to pay interest for. 

Borrowers would want to borrow more if they were paid to borrow so firms would be likely to borrow to invest more and consumers would want to borrow to consume so this should increase Aggregate Demand.
However, negative interest charged to ordinary savers is an incentive to keep cash and not put your money into a bank  so the supply of funds that banks could lend to firms for investment will fall which will reduce Aggregate demand.....so a negative interest rate is not a straightforward solution to the slow recovery of economic growth (N.B. evaluation).