I already have the answers, just need to double check. Please show ALL working out. Thanks.

Problem 1): The price of a European call that expires in five months and has a strike price of $165 is $2.58. The underlying stock price is $161, and a dividend of $3 is expected in three months. The risk-free interest rate is 5% per annum (continuously compounded).

a. What is the price of a European put option on the same stock that expires in five months and has a strike price of $165?

b. Let us assume some mispricing now. Show in detail the arbitrage strategies and the arbitrage profit for the following two scenarios for the European put option price in tabular form: 1) Scenario 1: The European put price is $8.0. 2) Scenario 2: The European put price is $4.5