Silverleaf Investments, a U$.$S$.$ company, engages in a carry trade by borrowing Japanese yen $($JPY$)($where interest rates are currently low$)$ and investing in Australian dollars $($AUD$)($where interest rates are currently high$).$ Silverleaf uses $$200,000$ of its own funds and borrows an additional $10,000,000$ Japanese yen. It will pay $0\mathrm{.}2\%$ on its Japanese yen borrowed for the next $3$ months and will earn $2\%$ on funds invested in Australian dollars. Assume that the Japanese yen's spot rate is $$0\mathrm{.}0080,$ and that the Australian dollar's spot rate is $$0\mathrm{.}70($so the Australian dollar is worth $87\mathrm{.}50$ Japanese yen at this time$).$ Silverleaf uses today's spot rate as its best guess of the spot rate three months from now.

a$)$ Calculate Silverleaf's expected profits from its carry trade.

b$)$ Suppose the Japanese yen appreciated over the $3-$month period against both the Australian dollar and the U$.$S$.$ dollar. At the end of the investment period, the Japanese yen is worth $$0\mathrm{.}0081,$ and an Australian dollar is worth $83\mathrm{.}05$ Japanese yen. Under these conditions, what is Silverleaf's expected profits from its carry trade?