Suppose that you are age 25 now and you want to be a millionaire when you retire at age 65. You have 40 years to accumulate wealth. At the end of each year you can invest $4,000 in your retirement account till age 65. Please answer the following two questions:
(1) Suppose your money will be invested in the stock market. Historically, the U.S. stock market has earned an average annual return of 12%. To be conservative, we assume that the return on your investment for the next 40 years will be a constant of 10% each year. Can you become a millionaire by age 65? Please show your calculations.
(2) Suppose your money will be invested in U.S. government bonds. Assume that the return over the next 40 years will be a constant 8% each year. Can you become a millionaire by age 65? Please show your calculations.