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 retirement, how long will the money last? [Hint: Solve this in two steps, before retirement and after retirement.]
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