please solve...no information is missing

Question 4. (* 1ximum, 30 marks in total) a) A US investment firm receives an invoice of $200,000 from a UK consulting firm. The spot rate of pound when the invoice was received was $1.50. The invoice should only be paid six months from now. Forecasted spot rates six months from now are given as below: Forecasted rate Probability $1.43 0.20 $1.46 0.70 $1.52 0.10 The six-month forward rate is $1.47. A call option on pounds that expires in six months has an exercise price of $1.48 and a premium of $0.03. A put option on pounds that expires in six months has an exercise price of $1.49 and a premium of $0.02. Required: If the invoice is to be paid six months from now, illustrate by showing your calculations, whether the firm will be better off by using forward contract to hedge the forex transaction risk. (10 marks)