Please answer 5, 6 and 7

A stock has a price of 100. It is expected to pay a dividend of $2 per share at year-end. An at-the-money European put option with 1 year maturity sells for $7. If the annual interest rate is 5%. what must be the price of an at-the-money European call option on the stock with 1 war maturity. You buy a share of stock, write a 1-year call option with strike price X = $100 and buy a 1-year put option with strike price X = $100. The net outlay required to establish this portfolio is $97. The stock pays no dividends. What is the risk-free interest rate? Suppose today's stock price of Book.com is $100. With probability 60% the price will rise to $130 in one year and with probability 40% it will fall to $80 in one year. A European put option with a strike price of $90 and a time to expiration of one year sells at $ 4. What is the one-year risk free rate implied by no-arbitrage? What would be the no-arbitrage risk free rate if with a probability of 50% the price increases and with a probability of 50% it decreases, keeping all other values constant? Explain! Use the Black and Scholes file posted on Classes (under Excel files). We want to explore the effect of changing the time to expiration T from 1 to 2 years on the value of an in-the-money put option. Throughout this exercise we keep the stock price at S_0 = 40, the strike price at X = 70, the dividend rate at delta = 0. and the stock price volatility at sigma = 35%. For the interest rate r, consider various values. Show how the effect on the put price for T = 1 rightarrow 2 depends on the interest rate and explain intuitively why this happens. Confirm that the call price is always increasing in the time to expiration T