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# What is the value of bonds and the interest rate fluctuations for the Garraty Company?

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The Garraty Company has two bond issues outstanding. Both bonds pay \$100 annual interest plus \$1,000 at maturity. Bond L has a maturity of 15 years, and Bond S a maturity of 1 year.

a. What will be the value of each of these bonds when the going rate of interest is (1) 5 percent, (2) 8 percent, and (3) 12 percent? Assume that there is only one more interest payment to be made on Bond S.

b. Why does the longer-term (15 year) bond fluctuate more when interest rates change than does the shorter-term bond (1 year)?

#### Solution Preview

Please see the attached document for proper formatting.

(a) We use the formula VB = PMT * [1 - 1 ¸ (1 + k)n] ¸ k + M ¸ (1 + k)n
(1) k = YTM = 5%, n = 15 for long bond (L), and n = 1 for short bond (S), PMT = \$100, M = \$1000, PV = VB?
VL = \$100 * [1 - 1 ¸ (1.05)15] ¸ 0.05 + \$1000 ¸ (1.05)15 = \$100 * 10.3797 + \$1000 *(0.4810) = \$1518.97. Also, using a financial function, we have N = 15, I = 5, PMT = 100, FV = 1000, PV = ? = -1518.9829. So, VL = \$1518.98.

VS = \$100 * [1 - 1 ¸ ...

#### Solution Summary

The solution shows all the calculations for the value of bonds with differing interest rates as listed in the problem.

\$2.19