Consider the following facts about Australian dollar: The current spot exchange rate is AUD1.36/USD. Over the next 180 days, there is a 20% probability that the AUD will strengthen relative to the dollar by 4%, and there is a 80% probability that the AUD will weaken by 7%. Required: a. What is the expected future spot exchange rate of USD per AUD? (4 marks) b. Suppose that the 180-day forward rate is AUD1.40/USD. i) What contract would you make to speculate in the 180-day forward market by either buying or selling AUD 10,000? (3 marks) ii) Calculate your expected US dollar profit in the 180-day forward market using AUD 10,000 (forward speculation). (2 marks) c. Given that the rate of change in the exchange rate is conditionally normally distributed, if the standard deviation of the 180-day rate of appreciation of the AUD relative to the USD is 4%, what range covers 95.45% of your possible US dollar profits and losses? (6 marks)