Complete Problem 31 of Chapter 10 (shown below), and submit your work to your instructor. Show your calculations and the algebraic manipulation of the price equation for the bond. In addition to solving the problem, write a 100- to 200-word essay on the term structure of fixed income securities.

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: P = C_1/(1 + r_1 ) + (C_2 + Par value)/(1 + r_2 )^2 

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?