An Australian firm is due to pay USD $500,000$ in $6$ months to a firm in the United States. The following information is available:

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Spot exchange rate $($AUD$/$USD$)1\mathrm{.}600$

Six$-$month interest rate in Australia$4\mathrm{.}00\%$ per annum

Six$-$month interest rate in the United States$3\mathrm{.}00\%$ per annum

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$($i$)$ Calculate the AUD value of the payables under a money market hedge. In doing so$,$ clearly outline the steps required to perform the money market hedge.

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$($ii$)$ Assuming that uncovered interest parity holds, how much would the importer expect to pay if the position remains unhedged?