***This is from Investment and Financial Mathematics (IFM) course for Actuaries. Please give handwritten solution with ALL steps shown plus with description because I need to understand the process. I will give "thumbs-up" for clear and correct solution. Thanks in advance!***

A stock had quarterly dividends, paid at the end of 3 months and 6 months from now. You are given: (i) The stock price is 42 and quarterly dividends are 0.75. (ii) O=0.3. (iii) A 6-month European put option is written on the stock with strike price 40. (iv) The put option, if it is exercised, is exercised on the stock ex-dividend. (v) The continuously compounded risk-free rate is 0.04. Calculate the put option's premium with the Black-Scholes formula. (Answer: 2.75)