Question

The Blossom Department of Transportation has issued 25-year bonds that make semiannual coupon payments at a rate of 9.825percent. The current market rate for similar securities is 11.3 percent. Assume that the face value of the bond is $1,000.

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What is the current market value of one of these bonds?

What will be the bond’s price if rates in the market (i) decrease to 9.30 percent or (ii) increase to 12.3 percent?

How do the interest rate changes affect premium bonds and discount bonds? Bonds, in general, INCREASE OR DECREASE price when interest rates go up. When interest rates decrease, bond prices INCREASE OR DECREASE.

Suppose the bond were to mature in 12 years. What will be the bond’s price if rates in the market (i) decrease to 9.30 percent or (ii) increase to 12.3 percent? (Round answers to 2 decimal places, e.g. 15.25.)   

Answer 1

Assuming there is no typo in the question and coupon rate is 9.825%
Price of the bond=face value*coupon rate/yield*(1-1/(1+yield/2)^(2*years to maturity))+face value/(1+yield/2)^(2*years to maturity)

What is the current market value of one of these bonds?
=1000*9.825%/11.3%*(1-1/(1+11.3%/2)^(2*25))+1000/(1+11.3%/2)^(2*25)=877.829647

What will be the bond’s price if rates in the market
(i) decrease to 9.30 percent
=1000*9.825%/9.3%*(1-1/(1+9.3%/2)^(2*25))+1000/(1+9.3%/2)^(2*25)=1050.634403

(ii) increase to 12.3 percent?
=1000*9.825%/12.3%*(1-1/(1+12.3%/2)^(2*25))+1000/(1+12.3%/2)^(2*25)=808.9586687

How do the interest rate changes affect premium bonds and discount bonds?

Bonds, in general, DECREASE price when interest rates go up. When interest rates decrease, bond prices INCREASE.

Suppose the bond were to mature in 12 years. What will be the bond’s price if rates in the market
(i) decrease to 9.30 percent
=1000*9.825%/9.3%*(1-1/(1+9.3%/2)^(2*12))+1000/(1+9.3%/2)^(2*12)=1037.487402

(ii) increase to 12.3 percent?
=1000*9.825%/12.3%*(1-1/(1+12.3%/2)^(2*12))+1000/(1+12.3%/2)^(2*12)=846.8190641