You are attempting to value a put option with an exercise price

of $$101$ and one year to expiration. The underlying stock pays no

dividends, its current price is $$101,$ and you believe it has a $50\%$

chance of increasing to $$125$ and a $50\%$ chance of decreasing to $$77.$

The risk$-$free rate of interest is $5\%.$ Calculate the value of a put

option with exercise price $$101.($Do not round intermediate

calculations. Round your answer to $2$ decimal places.$)$Value of a put option