The common stock of the P$.$U$.$T$.$T$.$ Corporation has been trading in a narrow price range for the past month, and you are convinced it is

going to break far out of that range in the next $3$ months. You do not know whether it will go up or down, however. The current price of

the stock is $$85$ per share, and the price of a $3-$month call option at an exercise price of $$85$ is $$8\mathrm{.}00.$

a$.$ If the risk$-$free interest rate is $9\%$ per year, what must be the price of a $3-$month put option on P$.$U$.$T$.$T$.$ stock at an exercise price of

$$85?($The stock pays no dividends.$)($Do not round intermediate calculations. Round your answer to $2$ decimal places.$)$

Put$-$call parity

b$.$ What would be a simple options strategy to exploit your conviction about the stock price's future movements. How far would it have

to move in either direction for you to make a profit on your initial investment? $($Round your intermediate calculations and final answer

to $2$ decimal places.$)$