Randy Hill wants to retire in $40$ years with $$1,000,000.$ If he can earn $9\mathrm{.}6\%$ APR on his investments, how much does he need to deposit each month to reach his goal?

Group of answer choices

$$178\mathrm{.}49$

$$552\mathrm{.}13$

$$350\mathrm{.}00$

$$250\mathrm{.}59$

None of the above