You need to save $$500,000$ for retirement. You plan on retiring in $20$ years. Your account earns $4\%$ interest. After you retire you plan on pulling out funds each month for $25$ 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?Make sure your work shows how you are solving the problems, but feel free to use your calculator extensively $-$ you don't need to show detailed steps of the formula evaluation.