You want to be a millionaire when you retire in $40$ years.

a$.$

How much do you have to save each month if you can earn an APR of $10\mathrm{.}9$ percent? $($Do not round intermediate calculations and round your answer to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$

b$.$ How much do you have to save each month if you wait $10$ years before you begin your deposits? $($Do not round intermediate calculations and round your answer to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$

c$.$ How much do you have to save each month if you wait $20$ years before you begin your deposits? $($Do not round intermediate calculations and round your answer to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$