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# Investments: Estimating the Price of a Bond

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An investor has 2 bonds in his portfolio that have a face value of \$1000 and pay a 10% annual coupon. Bond L matures in 15 years, while Bond S matures in 1 year.

A. What will the value of each bond be if the going interest rate is 5%, 8%, 12%? Assume that only one more interest payment is to be made on Bond S at its maturity and that 15 more payments are to be made on Bond L.

B. Why does the longer-term bond's price vary more than the price of the shorter-term bond when interest rates change?

#### Solution Preview

A. What will the value of each bond be if the going interest rate is 5%, 8%, 12%? Assume that only one more interest payment is to be made on Bond S at its maturity and that 15 more payments are to be made on Bond L.

Case : Interest Rate=5%
For Bond L,
Number of coupon payments=n=15
Coupon amount=C=1000*10%=\$100
Maturity amount=M=\$1000
Interest Rate=r=5%
Value of Bond L= C/r*(1-1/(1+r)^n)+M/(1+r)^n=100/5%*(1-1/(1+5%)^15)+1000/(1+5%)^15=\$1518.98

For Bond ...

#### Solution Summary

In about 215 words, this solution provides the formulas and variables required to calculate the value of a bond at various interest rates. Additionally, an explanation regarding long-term bond prices vs. short-term bonds with regards to changing interest rates is explored.

\$2.19