Hi! Hope you are doing great!

Can you help me out to solve this questions?

1. 1.) 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 year maturity.
2. 2.) Consider the following portfolio. You write a put option with exercise price 90 and you buy a put option on the same stock with the same expiration date with exercise price 95.

(a) Plot the payoff of the portfolio at the expiration date of the options.

(b) Which option must cost more and why? Make your argument using no-arbitrage rea- soning. On the same graph, plot how the profit of the portfolio would appear relative to its payoff.

3.)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?