I Options

d$.$ Consider a stock with a current price of $P=$$$27.$ Suppose that over the next $6$ months the stock price will either go up by a factor of $1\mathrm{.}41$ or down by a factor of $0\mathrm{.}71.$ Consider a call option on the stock with a strike price of $$25$ that expires in $6$ months. The risk$-$free rate is $6\%.$

$(1)$ Using the binomial model, what are the ending values of the stock price? What are the payoffs of the call option?

$(2)$ Suppose you write one call option and buy $N_s$ shares of stock. How many shares must you buy to create a portfolio with a riskless payoff $($i$.$e$.,$ a hedge portfolio$)?$ What is the payoff of the portfolio?

$(3)$ What is the present value of the hedge portfolio? What is the value of the call option?

$(4)$ What is a replicating portfolio? What is arbitrage?

Please please can you type the answers for each question that wouod help me understand what the answers better thank you I appreciate.