All interest rates are annual interest rates with semi-annual compounding. All coupon rates are annual rates paid semi-annually. All bonds have a $100 face value. Keep at least 6 decimal digits in all your calculation and answers unless specified otherwise.

Problem 1 (16 points): Assume that: Forward rates for 6 month and 1 year are r(0.5)=7% and r(1)=8%; Spot rates for 18 months and 2 years are (1.5)=7.8% and (2)=8.2% The price of a zero-coupon bond maturing 2.5 years from now is $81.50 a) (3 points) Find the 1-year spot rate (1). b) (3 points) Find the 18-month forward rate r(1.5) c) (3 points) Find the price of a 10% coupon bond maturing 2 years from now d) (3 points) Find 2.5 years forward rate r(2.5) e) (4 points) Assume 2-year 5% coupon bond and 2-year 7% coupon bond are priced correctly while 2-year zero coupon bond is incorrectly priced at $85. 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)