Suppose that the price of a non-dividend-paying stock is $32, its volatility is 30%, and the risk- free rate for all maturities is 5% per annum. In each case below, provide a table showing the relationship between profit and final stock price. Ignore the impact of time value of money.

a. A bull spread using European call options with strike prices of $25 and $30 and a maturity of six months. b. A bear spread using European put options with strike prices of $25 and $30 and a maturity of six months

c. A butterfly spread using European call options with strike prices of $25, $30, and $35 and a maturity of one year. d. A butterfly spread using European put options with strike prices of $25, $30, and $35 and a maturity of one year.

e. A straddle using options with a strike price of $30 and a six-month maturity. f. A strangle using options with strike prices of $25 and $35 and a six-month maturity.