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# Bond prices and maturity time

Bond X is a premium bond making annual payments. The bond pays an 8 percent coupon, has a YTM of 6 percent, and has 13 years to maturity. Bond Y is a discount bond making annual payments. This bond pays a 6 percent coupon, has a YTM of 8 percent, and also has 13 years to maturity.

If interest rates remain unchanged, what do you expect the price of these bonds to be one year from now? In three years? In eight years? In 12 years? In 13 years? What's going on here? Illustrate your answers by graphing bond prices versus time maturity.

#### Solution Preview

Please refer attached file for missing graph.

Let us assume par value of each bond=\$1000

Bond X
Coupon Amount=C=1000*8%=\$80
Maturity amount=M=\$1000
Required rate of return=r=YTM=6%
Case 1, Price in one year
Number of coupon payment left=n=13-1=12
Price of bond= C/r*(1-1/(1+r)^n)+M/(1+r)^n=80/6%*(1-1/(1+6%)^12)+1000/(1+6%)^12=\$1167.68
Case 2, Price in three years
Number of coupon payment left=n=13-3=10
Price of bond= C/r*(1-1/(1+r)^n)+M/(1+r)^n=80/6%*(1-1/(1+6%)^10)+1000/(1+6%)^10=\$1147.20
Case 3, Price in eight years
Number of coupon payment left=n=13-8=5
Price of bond= ...

#### Solution Summary

Solution analyzes the effect of maturity time on bond prices.

\$2.19