# 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-

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 one-page essay on the term structure of fixed income securities. Format your essay per APA style guidelines.**

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?