You have taken out a $$400,000,$ one$-$year ARM. The teaser rate in the first year is $5\mathrm{.}25\%($annual$).$ The index interest rate after the first year is $5\mathrm{.}50\%$ and the margin is $2\mathrm{.}75\%.($Note: The term on this ARM is $25$ years.$)$ There is also a periodic $($annual$)$ rate cap of $1\mathrm{.}50\%.$ Given this information, determine the monthly mortgage payment you would be scheduled to make in month $13$ of the mortgage loan$$s term.