The Federal Reserve Board can change interest rates it charges for loans to banks. This is the discount rate. Banks pay this rate to the Federal Reserve when they borrow money for the short term. In addition, the Fed sets a target date for money that banks lend to one another; it's called the target rate. Bond issuers set rates based on the Fed target rate plus a premium.
Treasury Bonds at Auction
The U.S. Treasury does not set Treasury bond rates. These bonds are sold at auction. The Fed target rate affects Treasury bonds by influencing demand. Less expensive rates increase demand, and more expensive rates decrease demand. The lower the demand, the higher the rates. This demand works at Treasury bond actions, as bidders set their prices based on their perception of the overall demand for the bonds.
Fed Sales of Bonds
The Fed buys and sells Treasury bonds. It raises or lowers the rates on those bonds according to the direction it wants interest rates to move. Buyers who did not get Treasury bonds in the government auction must pay the rate the Fed sets for selling its bonds.
Corporations can set their own bond rates, without directives from the Fed. In practice, however, a corporation that wants investors to buy its bonds sets a rate that's higher than the Fed target rate. There is no exact formula for this. The rate depends on the financial health of the company, plus the market's perception of what a fair bond rate would be in exchange for taking on the risk of buying the company's bonds. Since Treasury bonds are considered relatively safe, investors want a higher rate from corporations to buy their bonds.
Each municipality that issues bonds can set the interest rate. However, this rate tends to be tied to the Fed target rate policy. Since municipal bonds are exempt from federal tax, they usually have a lower yield to reflect the tax savings a buyer would get. Since the Fed target rate affects Treasury bonds, and municipal bonds generally follow the direction of Treasury bond rates, the Fed has an influence on municipal bond rates. The issuing municipality may set its rate based on any factors it wants to, but practical considerations of the marketplace tend to keep municipal bond rates moving in the same direction as other bond rates.
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