Suppose the risk-free rate today is 9.5%, and that in 10 months the Federal Reserve will change the rate to either 6.5% or 12.9%. In the risk-neutral world, assume that each is equally likely to happen with 50% chance. Compute the price of a European put option on the 11 month bond with face value $97.00, where the option expires in 10 months and the option's strike price is $89.64. Note that this means the bond matures 11 months after the option's expiration date and pays the bond holder $97.00 at the bond's maturity.