Pat receives a series of four annual federally subsidized student loans, each for $$5100$ at $6\mathrm{.}9\%.$ To defray rising costs for her senior year, $3$ years after acquiring the first loan she takes out a private student loan for $$3800$ at $7\mathrm{.}7\%$ interest with a term of $10$ years and capitalizes the interest for her last year of college. She graduates $9$ months after getting the private loan. Payments on all loans are deferred until $6$ months after graduation. Find her monthly payment.