At the age of $23,$ and you were able to land a great job paying $$55,000$ per year. To plan for your retirement, certain assumptions must be made. The first is that you will work for $42$ years, and you expect to receive annual pay increases of $3\%.$ This is $42$ years of receiving an annual income. Second, you plan to save $10\%$ of your annual salary. You further expect that you will be able to earn an average rate of $9\%$ on your investments during your working years. When you retire, you will reduce your tolerance for risk and expect a return of $6\%$ on your accumulated investments. If you plan to live $20$ years after retirement, how much monthly income can you expect, assuming you want to leave $$1,000,000$ to your heirs.