An investor wants to purchase a portfolio consisting of long a call with exercise price E = 190, and short a call with exercise price E = 220, both to be exercised on the same date in 6 months time. The investor expects that the share price S(T) on the exercise date will be 183 with probability 0.2, 198 with probability 0.5, and 236 with probability 0.3. If the initial cost to invest in the portfolio was 12, and the risk free interest rate is of the form r(t) = 0.01 +0.04t, find the expected profit for the investor.