$1)$ The Singapore dollar$$U$.$S$.$ dollar $($S$$/$$$)$ spot exchange rate is S$$20/$$$,$ the Canadian dollar$$U$.$S$.$ dollar $($CD$/$$$)$ spot rate is CD $8/$$$,$ and the Singapore dollar$-$Canadian dollar spot exchange rate is S$ $2\mathrm{.}60/$CD$.$

$$ a$)$ Figure out the correct cross exchange rate for Singapore dollar against Canadian dollar $($S$$/$CD$)$ that eliminates a triangular arbitrage. $(20$points$)$

$$ b$)$ You plan to exploit the triangular arbitrage opportunity when you have $$1$mil. to invest. $$

i$)$ Given the difference between the spot market exchange rate and the correct cross exchange rate, which currency is overpriced$/$overvalued on the spot market? Canadian dollar or Singapore dollar? $(20$points$)$

$$ ii$)$ How many Singapore dollars can you buy or sell in exchange for Canadian dollars when you exploit the arbitrage opportunity using $$1$mil.? $(20$points$)$

iii$)$ Figure out your profit in U$.$S$.$ dollars. $(20$points$)$