You need to save $$300,000$ for retirement. You plan on retiring in $20$ years. Your account earns $10\%$ interest. After you retire you plan on pulling out funds each month for $15$ years.

$($a$)$ How much do you need to deposit each month so that you can retire?

$($b$)$ How much interest will you have earned before retiring?

$($c$)$ How much will you be able to withdraw each month while in retirement?

$($d$)$ How much interest will you have earned during retirement?

$($e$)$ How much total interest would you have earned throughout this process?