Construct a short rate lattice for periods (years) 0 through 9 with an initial rate of \(6 \%\) and with successive rates determined by a multiplicative factor of either \(u=1.2\) or \(d=9\). Assign the risk-neutral probabilities to be .5 .

(a) Using this lattice, find the value of a 10 -year \(6 \%\) bond.

(b) Suppose this bond can be called by the issuing party at any time after 5 years. (When the bond is called, the face value plus the currently due coupon are paid at that time and the bond is canceled.) What is the fair value of this bond?