a$)$ The Australian dollar is currently worth $0\mathrm{.}6100$ US dollars and this exchange rate has a volatility of $12\%.$ The Australian risk$-$free rate is $7\%$ and the US risk$-$free rate is $5\%.$ Compute the value of a $3-$month American call option with a strike price of $0\mathrm{.}6000$ using a three$-$step tree.