1. A 1000 par-value bond with a 6% annual coupon rate matures in 3 years. You are given the one-year annual spot interest rate is 7%. The two-year annual spot interest rate is 8%. The one-year forward rate for year 3 is 9%. Calculate the price of the bond.
2. You are given the following spot rates:
Years to Maturity 1 2 3 4 5
Spot Rate 4.00% 4.50% 5.25% 6.25% 7.5%
You enter into a 5-year interest rate swap with a notional amount of 100,000 to pay a fixed rate and to receive a floating rate based on future 1-year LIBOR rates. If the swap has annual payments, what is the fixed rate you should pay?