The following prices are available for call and put options on a stock priced at $50. The risk-free rate is 6 percent and the volatility is 0.35.The March options have 90 days remaining and the June options have 180 days remaining.The Black-Scholes model was used to obtain the prices.

Assume that each transaction consists of one contract (100 options) unless otherwise indicated.

(a) What is the profit from a bull money spread using the March 45/50 calls if the stock price at expiration is $47?Suppose you close the spread 60 days later.What will be the profit if the stock price is still at $50?

(b) Suppose you expect the stock price to remain at about $50 and decide to execute a butterfly spread using the June calls. What will be the profit if the stock price at expiration is $52.50?

(c) Suppose you execute a calendar spread based on the assumption that stock prices are expected to remain fairly constant. Use the June/March 50 call spread.Assume one contract of each. What will be the profit if the spread is held 90 days and the stock price is $45?