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) Find the 1-year spot rate (1).

b) Find the 18-month forward rate r(1.5)

c) Find the price of a 10% coupon bond maturing 2 years from now

d) Find 2.5 years forward rate r(2.5)

e) 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)