"new money" is not, or ever, given to anyone. Banks included. The U.S. gov basically sells promissory notes (treasuries) to an independent, non governmental organization (The Federal reserve...which is not "federal" in the least bit..) on behalf of the American people. Although the fed is more or less offering a note at x price and the U.S. Treasury just buys it...
Anybody is allowed to buy bonds from the U.S. Treasury. In exchange, you get the "new money" as you call it. At no one point is anything given to the banks or asset holders.
The interest rate is determined by the rate the fed sets and buys these notes from the US T. This is the key and primary tool at which a PRIVATE, non-governmental organization, determines interest rates. However..you can also buy these notes directly from the Fed. China does all the time along with many other countries. Yes...other countries hold the "debt" of the American people... If that's not crazy enough...it gets better. This organization..the Fed...gets to tell banks how much to hold in required reserves. Another primary tool they use to control inflation.
