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 15% per annum. Use Black and Scholes pricing formula to calculate the cost of setting up the following positions:

1.A bull spread using European call options with strike prices of $25 and $30 and a maturity of 6 months

2. A butterfly spread using European call options with strike prices of $25, $30, and $35 and a maturity of 1 year

In each case provide a table showing the relationship between profit and final stock price. Ignore the impact of discounting.