Please show your work.

Question 4 (20 points) Assume that a bond has a sinking fund provision where the issuer can satisfy the sinking fund requirement by making a cash payment of the face amount of the bonds to be retired to the corporate trustee, who then calls the bonds for redemption using a lottery. The bond has a 4% coupon rate paid annually, a four-year maturity and a $500 million face value. The sinking fund requires retiring one fourth of the outstanding bonds at the end of each of the next four years. Given that the one-year zero rate is 3%, the two-year zero rate is 4%, the three-year zero rate is 5%, and the four-year zero rate is 6% (all rates are annual rates): a) What is your estimate of the market value of the bond today per $100 of face? b) What rate of return would you make on the bond if the bond you own is retired by lottery in two years