Consider 6-month spot interest rates evolving in the following two-step binomial tree over 12months, i.e., with 6 months in each of the next two steps. The current 12-month spot interest rate is 5.15% and the 18-month spot interest rate is 5.3%. Find the following by assuming monthly compounding. 12. The risk neutral probability for the up move in first step. 13. The risk neutral probability for the up move in second step. 14. The current fair value of a 6-month European call option with a strike price of $974 written on a 12-month zero coupon bond with face value $1000. 15. The current fair value of a 12-month European put option with a strike price of $994 written on a 18-month zero coupon bond with face value $1000.