Consider a stock priced at $30 with a standard deviation of 0.3. The risk-free rate is 0.05. There are put and call options available at exercise prices of 30 and a time to expiration of six months. The calls are priced at $2.89 and the puts cost $2.15. There are no dividends on the stock and the options are European. Assume that all transactions consist of 100 shares or one contract (100 options). Use this information to answer questions 1 through 10. show your work 1. What is your profit if you buy a call, hold it to expiration and the stock price at expiration is $37? 2. What is the breakeven stock price at expiration on the transaction described in problem 1? 3. What is the maximum profit on the transaction described in problem 1? 4. What is the maximum profit that the writer of a call can make? 5. Suppose the buyer of the call in problem 1 sold the call two months before expiration when the stock price was $33. How much profit would the buyer make? 6. Suppose the investor constructed a covered call. At expiration the stock price is $27. What is the investor's profit? 7. What is the breakeven stock price at expiration for the transaction described in problem 6? 8. If the transaction described in problem 6 is closed out when the option has three months to go and the stock price is at $36, what is the investor's profit? 9. What is the maximum profit from the transaction described in Question 6 if the position is held to expiration? 10. What is the minimum profit from the transaction described in Question 6 if the position is held to expiration? show your work