Note the following: All interest rates are annual interest rates with semi-annual compounding. All coupon rates are annual rates paid semi-annually. All bonds have $100 face values. Keep at least 6 decimal digits.

= Assume that: The spot rates for 6 months, 1 year, and 2 years are f(0.5) = 8% , f(1) = 9%, and f(2) = 10% respectively; The forward rate for 18 months is r(1.5) = 8.4% The price of a zero-coupon bond maturing 2.5 years from now is $79.80 a) (3 points) Find the 1-year forward rate r(1). b) (3 points) Find the 18-month spot rate f(1.5) c) (3 points) Find the price of a 9% coupon bond maturing 2 years from now d) (3 points) Find the 2.5-year forward rate r(2.5) e) (4 points) Assume 2-year 5% coupon bond and 2-year 8% coupon bond are priced correctly while 2-year zero coupon bond is incorrectly priced at $98.30. You want to make an arbitrage by trading only these 3 bonds. Find an arbitrage strategy (i.e., state how many of each bond you want to buy or sell) = Assume that: The spot rates for 6 months, 1 year, and 2 years are f(0.5) = 8% , f(1) = 9%, and f(2) = 10% respectively; The forward rate for 18 months is r(1.5) = 8.4% The price of a zero-coupon bond maturing 2.5 years from now is $79.80 a) (3 points) Find the 1-year forward rate r(1). b) (3 points) Find the 18-month spot rate f(1.5) c) (3 points) Find the price of a 9% coupon bond maturing 2 years from now d) (3 points) Find the 2.5-year forward rate r(2.5) e) (4 points) Assume 2-year 5% coupon bond and 2-year 8% coupon bond are priced correctly while 2-year zero coupon bond is incorrectly priced at $98.30. You want to make an arbitrage by trading only these 3 bonds. Find an arbitrage strategy (i.e., state how many of each bond you want to buy or sell)