Corbin wants to accumulate $$1,200,000$ over the next $20$ years by investing the same amount at the beginning of each month if he can expect a long$-$term rate of return of $8\mathrm{.}2\%$ compounded annually, how much must he invest each month? $($Do not round intermediate calculations and round your final answer to $2$ decimal places.$)$

Corbin must invest $ $$ at the beginning of each month.