Consider the following foreign exchange problem. The current one period $ interest rate $(r_{\text{\$}})$ is $6\%$ and the current one period $$ interest rate $(r_l)$ is $30\%.$ The British government have pegged the exchange rate to remain between the following values for the foreseeable future: $$0\mathrm{.}951\mathrm{.}00$$$1\mathrm{.}05.$

a$)$ Given this information, construct an arbitrage strategy for the next period and calculate the minimum expected profit from this strategy. Do you have any concerns about your strategy?

b$)$ Consider the case where the value of $1$ varies between $$d($lower bound$)$ and upper bound$),$ and the known one$-$period interest rates are $r_{\text{\$}}$ and $r_l.$ For there to be no arbitrage opportunities, what must be the relationship between $u,d,r_{}$ and $r_f?$