Problem 1 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 2.5 years forward rate r(2.5)

B) (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)