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

of $$109$ and one year to expiration. The underlying stock pays no

dividends, its current price is $$109,$ and you believe it has a $50\%$

chance of increasing to $$130$ and a $50\%$ chance of decreasing to $$88.$

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

option with exercise price $$109.$THE ANSWER IS NOT $10,$ or $9\mathrm{.}31$