$3.[5]$ Currently, the spot exchange rate is $$0\mathrm{.}85/$A$ and the one$-$year forward exchange rate is $$0\mathrm{.}81/$A$$.$ One$-$year interest is $3\mathrm{.}5\%$ in the U$.$S$.$ and $4\mathrm{.}2\%$ in Australia. You can borrow up to $$1,000,000$ or A$ $1,176,471,$ which is equivalent to $$1,000,000$ at the current spot rate

a$.$ Determine if IRP holds $($exactly$)$ between Australia and the United States

b$.$ If IRP doesn$$t hold, explain in detail how you would realize certain profit in U$.$S$.$ dollar terms.

c$.$ Explain how IRP will be restored because of the arbitrage transactions you carry out above.