Assume that forward rates for the next year are given by r(0.5)=6% and r(1)=7% and consider an 8% coupon bond maturing 1 year from now.

a) Find the bond price. Keep at least 6 decimal digits while doing calculations and reporting the answer.

b) Assume at t=0.5 the half-year spot rate will be exactly 7%. Find the price of the bond at t=0.5.

c) Assume at t=0.5 the half-year spot rate can be either 5% or 9% with equal probabilities. Find the expected price of the bond at t=0.5.

d) Assume at t=0.5 the half-year spot rate can be either (7-x)% or (7+x)% with equal probabilities, where 0