Using the risk neutral option valuation approach calculate the price of a six month put option on this stock with a strike price of $$85.$ Note that we are considering three states of the economy after six months. Boom neutral in bust. The risk neutral probability of the economy booming after six months is $40\%$ and the risk neutral probability of the economy staying neutral after six months is $50\%.$ Assume that the risk free rate is $10\%$ per year also assumed that the stock does not pay a dividend.