$.$ Assume you are given the following exchange rates S$\_\{$t$\}=1\mathrm{.}054$~USD$/$EUR and S$\_\{$t$\}=1\mathrm{.}369$~AUD$/$EUR

i$.$ What is the cross rate USD$/$AUD$?$

ii$.$ Suppose the $180-$day forward rate is F$1,180-1\mathrm{.}08$ USD$/$EUR$.$ Calculate the forward premium. Does the forward rate contain a premium or a discount?

iii. Suppose Kwiki Bank quotes S$\_\{$f$\}=\mathrm{.}81$~USD$/$AUD Is arbitrage possible? $($Why$?)$

iv$.$ If yes, describe a triangular arbitrage strategy and determine an arbitrageur's profits