You plan to retire 40 years from now. Once you retire, you want to be able to withdraw $180,000 a year (starting one year after you retire) for another 30 years and still have $1,000,000 left in the account afterwards. You plan to meet your retirement goals by making equal annual deposits at the end of each year for the next 40 years. In addition, you have $20,000 in cash that you plan to invest in the same retirement account today. You expect that you will be able to earn 12% per year on your deposits for the first 40 years. However, you expect to earn only 6% per year on your investment after you retire since you will choose to place the money in less risky investments. (Show the basic formulas you rely on to answer the question. Also show the steps/etires you took to solve the problem, whether you used algebra, a calculator, or Excel.)

[Reminder: Draw the timeline for yourself and clearly identify all cash flows.]

a) How much money do you need to have when you reach retirement (40 years from now) in order to meet your goals? (10 points)

b) Find the equal annual deposits that you must make each year to reach your retirement goal. (10 points)