Problem 1 (20 points) Consider an annual coupon bond with a face value of $100,

Question

Problem 1 (20 points) Consider an annual coupon bond with a face value of $100, exactly four years to maturity and a 4% annual coupon. The bond is priced to yield 3.25% per year (annually compounded rate) a) Calculate the price of the bond. b) Calculate the bond's duration. c) Calculate the bond's modified duration. Make sure your answer accounts for the fact that the bond is an annual pay bond (not semiannual). d) Calculate the proportional change in the bond price if the bond yield changes from 3.25% to 3.5%. e) Compare the answer that you get in d) to the estimate of this proportional change that you can derive from the bond's modified duration.

Explanation / Answer

ANSWER A) PRICE OF BOND

Hence the price of the bond is 102.78

ANSWER B)

Duration = Total of product divided by total of DCF

=388.368 / 102.784

Duration =3.78 Years

Note: DCF = Discounted cash flow

PVF = Present value factor

Particulars Amount Period PVF @3.25% DCF Interest 4 1 to 4 years 3.695 14.78 Principal 100 4th year 0.880 88 PRICE OF BOND( TOTAL) 102.78

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