A stock has a current price of $$78.$ An option on this stock that expires in five months has an exercise price of $$75.$ The stock will pay a

dividend of $$3$ in three months. Assume an annualized volatility of $35\%$ and a continuously compounded risk$-$free rate of $3\%$ per

annum. Use the Black$-$Sholes$-$Merton model to price this option.

$($In all your calculations, round the numbers to $4$ decimal places.$)$

Suppose the option is a European put. Calculate the value of the put.

$

Suppose this option is an American call. Use Black's approximation to calculate the value of this call.

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