Suppose the price of 1-year maturity zero-coupon bonds with face value $1000 is $952.38 and the price of 2-year zeros with $1000 face value is $890. The price of 3-year zero-coupon bonds with face value $1000 is $816.30. The yield to maturity on the 1-yearbond is 5% and the yield to maturity on the 2-year bond is 6%.

a) What is the forward rate for the third year? (5points)

b) How would you construct a synthetic 1-year forward loan that commences at t=2 and matures at t=3? (10points)