Assume that forward rates for the next year are given by r(0.5)=7% and r(1)=9% and consider a 6% coupon bond maturing 1 year from now.

a) Find the bonds price.

b) Assume that at t=0.5 the half-year spot rate will be exactly 8%. Find the price of the bond at t=0.5.

c) Assume that at t=0.5 the half-year spot rate can be either 7% or 9% with equal probabilities so that the expected spot rate is 8%. Find the expected price of the bond at t=0.5. Is it higher, lower, or the same as the price you found in part (b)?