please show the workings

Problem 2 (5 points): Assume that forward rates for the next year are given by r(0.5)=7% and r(1)=6% and consider a 5% coupon bond matpring 1 year from now. a) (1 point) Find the bond price. b) (2 points) Assume at t=0.5 the half-year spot rate will be exactly 6%. Find the price of the bond at t=0.5. c) (2 points) Assume at t-0.5 the half-year spot rate can be either 5% or 7% with equal probabilities so that the expected spot rate is 6%. 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)