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 inter- est over its life. The interest rate on the bill is there- fore $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. S uppose, 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. ( Hint: The interest earned is $1,000 − P . What is the percentage interest rate?) Show that this formula illustrates the point made in the text: Higher bond prices mean lower interest rates.
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