Emily is planning to sell a forward contract on $180-$day bank bills, to be delivered at the end of $90$ days, with a face value of $$100000.$ The current spot rate for $90-$day bank bills is $1\mathrm{.}7\%$ p$.$a$.($simple interest$)$ and the current spot rate for $270-$day bank bills is $2\%$ p$.$a$.($simple interest$).$ Assume Emily can borrow or lend at the same rate as the yield rate of the bank bills.

a$.$ Use two carefully labelled cash flow diagrams in your answer to set out the cash flows associated with the forward contract and the replicating portfolio to 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 $2$ 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 $$100000$ is $1\mathrm{.}9\%$ p$.$a$.($simple interest$).$ List and explain all the steps that Emily 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. Round your answer to three decimal places.