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 $945. 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.