Assume the following information:

The current spot rate of the Australian dollar $=$ $$\mathrm{.}64$

The forecasted spot rate of the Australian dollar $1$ year from now $=$ $$\mathrm{.}59$

The $1-$year forward rate of the Australian dollar $=$ $$\mathrm{.}62$

The annual interest rate for the Australian dollar $=9\%$

The annual interest rate for the U$.$S dollar $=6\%$

Given the information above,

a$)$ Determine whether covered interest arbitrage $($CIA$)$ opportunity exists in the market. Please show your

detailed calculations and explanations. b$)$ If an investor can borrow $$500,000$ or its Australian dollar equivalent today to conduct covered

interest arbitrage, how much CIA profit can this investor make? Please show your detailed calculations

and explanations.