Emine Gul plans to retire $25$ years from today with the following goals;

$-$She would like to purchase a cottage $10$ years from today for $$250,000,$

$-$She would like to receive a monthly income of $$20,000$ per month for $25$ years, with the first payment received $25$ years and one month from now $($one month after retirement$),$

$-$ After $25$ years of withdrawals, she$$d like to leave an inheritance of $$800,000$ to her kids.

She is able to save $$4000$ a month for the next $10$ years. If she can earn $10\%$ EAR before she retires and $8\%$ EAR after she retires, how much will she have to save each month in years $11$ through $25?$