Sarah plans to purchase a forward contract on 180-day bank bills, to be delivered at the end of 90 days, with face value of $200,000. The current spot rate for 270-day bank bills is 3.26% p.a. (simple interest rate) and the current spot rate for 90-day bank bills is 3.15% p.a. (simple interest rate). Assume that Sarah can borrow or lend at the same rate as the yield rate of the bank bills. 

a.  Using two carefully labelled cash flow diagrams in your answer, set out the cash flows associated with the forward contract and the replicating portfolio. With reference to these diagrams, explain how you can determine the fair forward rate for this forward contract. Base your answer on the arbitrage pricing principle, and express the fair forward rate as an annual simple rate of interest, to two decimal places. 

b. Suppose that the forward rate for a forward contract on 180-day bank bills, to be delivered at the end of 90 days, with face value of $200,000, is 4% p.a. (simple interest rate). List and explain all the steps that Sarah needs to undertake in order to make an arbitrage profit from this forward contract. Make sure you outline all that needs to happen on all relevant dates, as well as today.

c.  Suppose that the forward rate for a forward contract on 180-day bank bills, to be delivered at the end of 90 days, with face value of $200,000, is 3% p.a. (simple interest rate). List and explain all the steps that Sarah needs to undertake in order to make an arbitrage profit from this forward contract. Make sure you outline all that needs to happen on all relevant dates, as well as today.