***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!***

For a stock, you are given: (i) The price is 45. (ii) The stock volatility is 0.2. (iii) The continuously compounded risk-free rate is 0.05. (iv) The continuous dividend rate of the stock is 0.02. A European put option with strike price 43 expires in 3 months. Using the Black-Scholes-Merton formula, how many shares of stock should be sold and how much should be lent, to replicate the put option? (Answer: 0.2797 and 13.41) For a stock, you are given: (i) The price is 45. (ii) The stock volatility is 0.2. (iii) The continuously compounded risk-free rate is 0.05. (iv) The continuous dividend rate of the stock is 0.02. A European put option with strike price 43 expires in 3 months. Using the Black-Scholes-Merton formula, how many shares of stock should be sold and how much should be lent, to replicate the put option? (Answer: 0.2797 and 13.41)