Buffelhead's stock price is $$228$ and could halve or double in each six$-$month period. Assume that you own a one$-$year American put option on Buffelhead stock with an exercise price of $$228.$ The interest rate is $21\%$ a year.

A$.$ Would you ever want to exercise an American put early?

B$.$ Calculate the value of the Buffelhead American put.

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

C$.$ Calculate the value of the put if it had been European$-$style.

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