The current price of the stock of Mont Tremblant Air is C $$109.$ During each six$-$month period it will either rise by $12\mathrm{.}0\%$ or fall by $10\mathrm{.}9\%$

$($equivalent to an annual standard deviation of $16\mathrm{.}0\%.$ The interest rate is $6\%$ per six$-$month period.

a$.$ Calculate the value of a one$-$year European put option on Mont Tremblant's stock with an exercise price of C$$113\mathrm{.}25.$

b$.$ Recalculate the value of the Mont Tremblant put option, assuming that it is an American option.

Note: Do not round intermediate calculations. Round your answers to $2$ decimal places.