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Homework 2 (Due: In class, Tuesday, 09/24/19) 1. a. A zero-coupon bond pays $1000 in five years. i) What is the value of the bond today? The nominal interest rate i is 3% ii) Price the bond if the interest rate is now 7 % . iii) Describe the relationship between the interest rate and the bond price b. A zero-coupon bond pays $1000 in one year and sells for $920 now. Calculate the yield to maturity of the bond. c. A zero-coupon bond pays $1000 in six years and sells for $750 now. Calculate the yield to maturity of the bond to the nearest basis point (one hundredth of one percent). d. A consol pays $20 each year forever. The consol is currently selling for $160. The consol begins payments next year. What is the yield to maturity of the consol? e. A one-period coupon bond has a face value of $FV and pays an annual coupon amount C. Show that if the bond is priced at par (that is, the bond price equals its face value), then the yield of the bond is the coupon rate c. f. An annual coupon bond has a maturity of twelve years, a face value of $1000, and a coupon rate of 4%. The current market price of the bond is $780. Use a grid search to find the yield to maturity of the bond to the nearest basis point (one hundredth of a percent). Other methods will not receive full credit. Use a spreadsheet program and print a copy of your work. g. A U.S. Treasury note with a face value of $1000 pays interest semiannually at matures in three years. If the coupon rate is 4% and the bond equivalent yield is 5%, find the price of the note Obey all pricing conventions. i) At the grocery store, apples cost 96 cents and bananas cost 92 cents. If a shopper buys twenty apples and ten bananas, what is the total cost at checkout? ii) A one year zero coupon bond with a face value of $100 has a yield of 4.1 667%. A similar bond with a maturity of two years has a yield of 4.2572%. If a bond manager holds a bond portfolio with twenty zero coupon bonds that mature in one year and ten zero coupon bonds that mature in two years, what is the value of the bond portfolio? iii) Compare part (i) to part (ii) in a sentence or two. i. Consider the prices for the following zero-coupon bonds: h. Price Face Value Maturity 1 year 2 year 3 year Bond 0.98 $1 Bond A 0.94 $1 Bond B 23 $25 Bond C Calculate the price of an annual coupon bond that matures in 3 years with a coupon rate of 5% on a face value of $100. (Problem 1, continued:) j. At the grocery store, you buy twenty apples and ten bananas. The price of an apple is twenty five cents, while your total bill is $9. What is the price of a banana? Explain your solution procedure using an equation. k. Suppose three bonds that pay annual coupons have a face value of $100 and are according to the following table: priced Price Maturity 1 year 2 years 3 years Coupon Rate Bond $96.89922 0% A $96.25466 2.5% $95.25892 5% Three zero coupon bonds with maturities of 1 year, 2 years, and 3 years have a face value of $1 each. Find the price of each zero coupon bond

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