Alon makes $$14,470/$month$.$ He is applying for a mortgage that requires at most $32\%$ front end PTI and $44\%$ back$-$end PTI. His other debt obligations are estimated to be around $$1,500/$month$.$ What is the maximum qualified mortgage payment that Alon can have? State your answer as a number rounded to the nearest cent $($e$.$g$.$ if you get $$1013\mathrm{.}57654,$ write $1013\mathrm{.}58)$