# interest rate

1. Suppose the Fed purchases \$5 billion worth of government bonds from Bill Gates, who banks at the Bank of America in San Francisco. Show the effects on the balance sheets of the Fed, the Bank of America, and Gates. Does it make any difference if the Fed buys bonds from a bank or an individual?

2. Treasury bills have a fixed face value (say, \$1,000) and pay interest by selling at a discount. For example, if a one-year bill with a \$1,000 face value sells today for \$950, it will pay \$1,000 – \$950 = \$50 in interest over its life. The interest rate on the bill is therefore \$50/\$950 = 0.0526, or 5.26 percent.

a. Suppose the price of the Treasury bill falls to \$925. What happens to the interest rate?

b. Suppose, instead, that the price rises to \$975. What is the interest rate now?

c. (More difficult) Now generalize this example. Let P be the price of the bill and r be the interest rate. Develop an algebraic formula expressing r in terms of P. Show that this formula illustrates the point made in the text: Higher bond prices mean lower interest rates.

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