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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

Hello!
The value of a bond is simply the present value of its stream of payments.

Let's call R to the interest rate. We know that bond L will pays \$100 per year. I'll assume here that this payment is done at the end of each year. So, when the bond matures (15 years from today) we'll receive a \$100 payment plus the \$1,000. The stream of payments from this bond is:

Year 1: \$100
Year 2: \$100
...
Year 15: \$100 + \$1,000 = \$1,100

Let's assume that we're at year 0, so the first payment on bond L will ...

\$2.19