Please Mainly Answer Part (C)

All interest rates are annual interest rates with semi-annual compounding. All coupon rates are annual rates paid semi-annually. All bonds have $100 face values. Keep at least 6 decimal digits.

Assume that forward rates for the next year are given by r(0.5)=7% and 1(1)=9% and consider a 6% coupon bond maturing 1 year from now. a) (1 point) Find the bond's price. b) (2 points) 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) (2 points) 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)