Marie is putting together a retirement plan and is scheduled to retire in $40$ years. She is planning to open a retirement account and invest an equal amount each month into the retirement account. If she expects to earn $10\mathrm{.}5\%$ per year in the account and is planning to have $$3,000,000$ in the account at retirement, what is the amount of the monthly investment?

$$407\mathrm{.}11$

$$474\mathrm{.}07$

$$667\mathrm{.}71$

$$743\mathrm{.}34$

None of the above