Solve using method of undetermined coefficients:

A college professor contributes $$5,000$ per year into her retirement fund by making

many small deposits throughout the year. The fund grows at a rate of $7\%$ per year

compounded continuously. After $30$ years, she retires and begins withdrawing from

her fund at a rate of $$3000$ per month. If she does not make any deposits after retire$-$

ment, how long will the money last? $[$Hint: Solve this in two steps, before retirement

and after retirement.$]$