$6.$ 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 $$0\mathrm{.}757/$A$$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{.}320/1.($LG $9-5)$

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 $$0\mathrm{.}715/$A$$1$ and $$1\mathrm{.}520/1,$ respectively?

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 $$200,000($disregarding any change in principal values$)?$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 $$\frac{0\mathrm{.}757}{A}$$$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 $$\frac{1\mathrm{.}320}{}1.($LG $9-5)$

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 $$\frac{0\mathrm{.}715}{A}$$$1$ and $$\frac{1\mathrm{.}520}{}1,$ respectively?

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 $$200,000($disregarding any change in principal

values$)?$