Carolyn has just retired, and has $250000$ dollars in her retirement account. The account will earn interest at an annual rate of $10$ percent, compounded monthly.

At the end of each month, Carolyn will withdraw a fixed amount to cover her living expenses. $($Give your answer in dollars, correct to the nearest cent.$)$

What is the maximum amount that Carolyn can withdraw each month if she wants her savings to last indefinitely?