Let x be a positive number and suppose that the annual Australian dollar interest rate is x$\%$ and the United States dollar annual interest rate is $5\mathrm{.}5\%.$ The spot rate for the United States dollar is $A$1\mathrm{.}58.$

$($a$)$ Using interest rate parity, calculate the forward rate premium of the United States dollar with respect to the Australian dollar in terms of x$.$

$($b$)$ Using your answer to $($a$),$ find x if the one$-$year forward rate for the United States dollar is A$$1\mathrm{.}55.$