Congratulations! Today is your 20^th birthday, but you are starting with nothing in the bank. You just started working full-time, earning $50,000 per year. Your goal is to have $5 million by your 60^th birthday (i.e., 40 years from today). Your employer offers a 401(k) plan (contributions by you are tax deductible, growth is tax deferred), and within that plan you choose to invest in an extreme low-cost S&P 500 index mutual fund (like ones offered by Schwab, Fidelity, Vanguard, etc.). The long-term expected return on the S&P 500 index mutual fund is 10% per year. Your employer pays you monthly.

(a) Ignoring taxes, if the employer offers no match on your contributions, how much would you need to save every month to reach your goal?

(b) Ignoring taxes, if the employer offers a 10% match on your contributions (meaning if you put up to 10% of your gross salary in, they will match your investment amount, but if you put in 11% they will only match 10%), how much would you need to save every month on top of your match to reach your goal?

(c) Assume your personal Federal marginal tax rate is 24% and personal State of Arkansas marginal tax rate is 6%. What is the answer to question (b) on an after-tax basis (i.e., how much do you have to contribute every month after the employer match and net of tax savings)? (Hint: contributions to a 401(k) plan are tax deductible, grow tax deferred, but withdrawals are taxed as regular income when you take money out.)

(d) All of the above amounts are nominal. If your inflation expectation is 3% per year, how much would you have to save every month after employer match, net of tax savings, and after accounting for inflation, to achieve a long-term goal of $10 million in todays (real) dollars by your 65^th birthday?

(e) Will your return likely be higher or lower than that of the S&P 500, and why? (Assume effectively zero expense fees with this low-cost indexed mutual fund and ignore taxes.)