You find that the one-, two-, three-, and four-year interest rates are 4.2 percent, 4.5 percent, 4.9 percent, and 5.1 percent. What is the yield to maturity of a four year bond with an annual coupon rate of 6.5 percent? Hint: Use the bootstrapping technique in Problem 31 to find the price of the bond.

Data From Problem 31

One method used to obtain an estimate of the term structure of interest rates is called bootstrapping. Suppose you have a one-year zero coupon bond with a rate of r₁ and a two-year bond with an annual coupon payment of C. To bootstrap the two-year rate, you can set up the following equation for the price (P) of the coupon bond:

Because you can observe all of the variables except r₂, the spot rate for two years, you can solve for this interest rate. Suppose there is a zero coupon bond with one year to maturity that sells for $949 and a two-year bond with a 7.5 percent coupon paid annually that sells for $1,020. What is the interest rate for two years? Suppose a bond with three years until maturity and an 8.5 percent annual coupon sells for $1,029. What is the interest rate for three years?

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C, + Par value C, P=T+r, (1 + r,)?