Sun Bank USA has purchased a $16$ million one$-$year Australian dollar loan that pays $12$ percent interest annually. The spot rate of U$.$S$.$ dollars for Australian dollars $($AUD$/$USD$)$ is $$0\mathrm{.}625/$A$$1.$ It has funded this loan by accepting a British pound $($BP$)$denominated deposit for the equivalent amount and maturity at an annual rate of $10$ percent. The current spot rate of U$.$S$.$ dollars for British pounds $($GBP$/$USD$)$ is $$1\mathrm{.}60/1.$

a$.$ What is the net interest income earned in dollars on this one$-$year transaction if the spot rate of U$.$S$.$ dollars for Australian dollars and U$.$S$.$ dollars for BPs at the end of the year are $$0\mathrm{.}588/$A$$1$ and $$1\mathrm{.}350/1,$ respectively? $($Negative amount should be indicated by a minus sign. Do not round intermediate calculations. Enter your answers in dollars, rather than in millions of dollars. Round your final answer to the nearest whole dollar. $($e$.$g$.,32))$

b$.$ What should the spot rate of U$.$S$.$ dollars for BPs be at the end of the year in order for the bank to earn a net interest income of $$230,000($disregarding any change in principal values$)?($Round your answer to $5$ decimal places. $($e$.$g$.,32\mathrm{.}16161))$