A student borrows $$75,000$ for business school at $7\mathrm{.}0\%$ stated annual interest with monthly repayment over $9$ years. Consider this as a loan with no payments or interest during school so that the problem structure is equivalent to a standard loan received one period before the first payment. Suppose that to better match expected student salary growth over time, the loan is structured as a growing annuity with each monthly payment growing by $0\mathrm{.}2\%$ compared to the previous monthly payment. How much is the first monthly payment?