A large commercial bank observes the annual return on $180-$day Canadian dollar denominated bonds $($RC$$)$ is $4\%$ and the annual return on $180-$day British pound denominated bonds $($R$)$ is $5\%.$ Suppose the spot $/$C$ exchange rate is $0\mathrm{.}55,$ and $$ is traded at a forward discount of $2\%$ per year.

Note: Keep your answers to $4$ decimal points if necessary.

a$)$ Find the $180-$day forward $/$C$ exchange rate. $(3$ points$)$

b$)$ Based on the above information, is there any arbitrage opportunity? If yes, describe how the commercial bank could capture this arbitrage profit. $(6$ points$)$

c$)$ Suppose the commercial bank has the ability to $$move$$ the market $($i$.$e$.$ affecting spot exchange rate, the forward exchange rate, and the returns on bonds in both countries$),$ what happens to these variables after the transactions in part $($b$)?$ Explain. $(8$ points$)$

d$)$ Instead of affecting the interest rates and the forward exchange rate as in part $($c$),$ now suppose the spot exchange rate bears all the burden of adjustments, find the spot $/$C$ exchange rate that would eliminate interest arbitrage. $(3$ points$)$