Assume that:

The spot rates for 6 months, 1 year, and 2 years are (0.5) = 8% , (1) = 9%, and (2) = 10% respectively;

The forward rate for 18 months is (1.5) = 8.4%

The price of a zero-coupon bond maturing 2.5 years from now is $79.80

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

2. Find the 18-month spot rate (1.5)

3. Find the price of a 9% coupon bond maturing 2 years from now points)

4. Find the 2.5-year forward rate r(2.5)

5. Assume 2-year 5% coupon bond and 2 year 8% coupon bond are priced correctly while the 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)