solution

You are doing some long-range retirement planning. On the day you retire (23 years from now) you want to be able to withdraw $200,000. Then, you want to withdraw the following amounts at the end of each year after that (during your retirement period).

Years 1-4 $160,000

Years 5-9 $175,000

Years 10-15 $165,000

Years 16-26 $145,000

At the end of the 26^th year in retirement, you’d like to have $500,000 remaining in your retirement account available for withdraw. During your retirement years, you anticipate earning a 4.5% rate of return.

You currently have $275,000 that you are going to use to start your retirement savings today. In addition, you plan to save $700 at the end of each month for the next 8 years. At that point (8 years from today) you will add another $150,000 to your retirement fund. Then, over the remaining 15 years, how much must you save at the end of each month to reach your goal if you earn 8.9% as a rate of return during the first 8 years and 7.6% over the final 15 years in which you are saving for retirement?