Actuarial FM question:

Please show steps, final answer is

a)call payoff = 0 when S_T=80 or 90, =10 when S_T=105

 call profit= -2.04 when S_T=80 or 90, =7.96 when S_T=105

  ?b) S_T> 107.0396

At time 0, the share price of a stock was $85. At that time, a call option on a share of stock with a strike price of $95 expiring 6 months later had a premium $2.00. Risk free interest is 4% annual effective. (a) Determine the payoff and the profit on the purchased call option on the expiry date for each of the following stock values at time T = 0.5: 80, 90, 105. (b) Determine the share price needed on expiry to obtain a profit on the purchased call option of at least $10.