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# Bootstrapping and Interest Rate Example Problem

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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?

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#### Solution Preview

What is the interest rate for two years?
\$1,020 = 1,000*7.5%/[1+(\$1,000-\$949)/\$1,000] + (\$1,000*7.5% + \$1,000)/(1 + r2)^2
\$1,020 = 75/[1+(\$51)/\$1,000] + (\$75 + \$1,000)/(1 + r2)^2
\$1,020 = 75/[1+5.1%] + (\$1,075)/(1 + r2)^2
\$1,020 = 75/1.051 + (\$1,075)/(1 + ...

#### Solution Summary

This solution provides assistance with determining the interest rate for each of the problems.

\$2.49