A European call with X$=80$ and the time to expiration $($T$)$ of $1$ year currently sells for $$10($C$0).$ The underlying stock price, S$0,$ is $$85.$ The risk$-$free interest rate is $5\%.$ You are considering purchasing a European put option with the same exercise price and expiration date.

$3)$ The European put option price$($P$0)$ is currently $$0\mathrm{.}50.$ Does it violate Fact $3($Put$-$Call Parity$)?$ If so$,$provide your arbitrage strategy.

$4)$ What is your today$$s profit $($cash flow$)?$

$5)$ What is your profit $($cash flow$)$ on the expiration date if ST$=70?$ Describe your actions to have each cash flow for your profit on the expiration date.