$3.$ Arbitrage $(10$ points$)$ The YTM on a $6-$month Zero is $\backslash (5\backslash \%\backslash ).$ The YTM on a $1-$year Zero is $\backslash (6\backslash \%\backslash ).$ Zeros have face value $\backslash (=\backslash$$ $100\backslash ).$ The YTM on a $1-$year $\backslash (12\backslash \%\backslash )($coupon rate$)$ Treasury note $($paying semiannual coupon payments$)$ is $\backslash (5\mathrm{.}8\backslash \%\backslash ).$ Assume the note has $\backslash (\backslash$$ $1,000\backslash )$ face value. What is the arbitrage opportunity and what is the profit? $($Hint: first calculate the price of the $\backslash (12\backslash \%\backslash )$ Treasury note and then the price of replicating the $\backslash (12\backslash \%\backslash )$ Treasury note cash flows instead with Zeros$)$