Problem $9-6($LG $9-5)$

Sun Bank USA has purchased a $32$ 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 $$0\mathrm{.}625/$A $$.$ 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 $$\frac{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 $$\frac{0\mathrm{.}588}{A}$$$1$ and $$\frac{1\mathrm{.}850}{}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 $$340,000($disregarding any change in principal values$)?($Round your answer to $5$ decimal places. $($e$.$g$.,32\mathrm{.}16161))$

$\backslash$table$[[,],[$a$.,$Net interest income,$],[$b$.,$Spot rate of U$.$S$.$ dollars,$]]$