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There is a European put option on a stock that expires in two months. The stock price is $$89$ and the standard deviation of the stock returns is $69$ percent. The option has a strike price of $$96$ and the risk$-$free interest rate is an annual percentage rate of $5\mathrm{.}2$ percent. What is the price of the put option today? Use a two$-$state model with one$-$month steps. $($Do not round intermediate calculations and round your answer to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$