Why would you borrow to hoard?
EDIT: And you were talking about the fed buying bonds, not lending.
In my understanding, FED first produce 1B money to buy bonds, and these bonds will become FED's reserve and enable FED to loan 10B money to commercial bank at 0 interest. Commercial banks are happy to borrow at 0 interest (free money), but they have a difficulty to loan out these money due to many of the companys already scared by financial crisis and are not willing to take loan due to uncertain business condition
In my understanding, when the fed buys 1B in bonds, the government then spends this 1B in bonds and the money enters the economy.
The bonds are the "reserve" for those 1B.
When the fed lends to commercial banks 10B, the "reserve" is an IOU from commercial banks stating "IOU 10B plus interest". But if the inflation is equal to the nominal interest, then the real interest is zero.
The fed doesn't use fractional reserve, because all its "reserves" are always debt .
You talk like if creating price inflation was a hard thing to do, but is the simplest thing in the world. Is the government of zimbawe made of geniuses because they reach hyperinflation?
No.
M * V = P * Q
You increase M, P will increase. Period.
Creating price inflation is just as easy as print (creating monetary inflation).