2. (20 points) 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 70^th birthday (i.e., 50 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 every two weeks.

a. How much would you need to save every two weeks to reach your goal?

b) If your employer offers a 1 for 1 match on up to 10% of your pay for your own 401(k) contributions, how much would you need to save every two weeks on top of your match to reach your goal?

c) Assume your Federal marginal tax rate is 22% and State 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 after the employer match and net of tax savings)?

d) If your inflation expectation is 4% per year, how much would you have to save after employer match, net of tax savings, and after accounting for inflation, to achieve a long-term goal of $5 million in todays (real) dollars by your 70^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.)