2. (20 points) Congratulations! Today is your 20th 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 $2 million by your 65 birthday (i.e., 45 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) lgnoring 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 match of 5% on your contributions, how much would you need to save every month on top of your match to reach your goal? (c) Assume your Federal marginal tax rate is 24% and State marginal tax rate is 6.9%, 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) All of the above amounts are nominal. If your inflation expectation is 2% 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 $2 million in today's (real) dollars by your 65th birthday? (e) Now you are retired and living off your more than $2 million investment, still invested in the S&P 500 mutual fund. Will your return before and after retirement likely be higher or lower than that of the S&P 500, and why? (Assume effectively zero management expense fees (you can now do this with one of Fidelity's mutual funds) with this extreme low-cost indexed mutual fund and ignore taxes). 2. (20 points) Congratulations! Today is your 20th 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 $2 million by your 65 birthday (i.e., 45 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) lgnoring 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 match of 5% on your contributions, how much would you need to save every month on top of your match to reach your goal? (c) Assume your Federal marginal tax rate is 24% and State marginal tax rate is 6.9%, 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) All of the above amounts are nominal. If your inflation expectation is 2% 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 $2 million in today's (real) dollars by your 65th birthday? (e) Now you are retired and living off your more than $2 million investment, still invested in the S&P 500 mutual fund. Will your return before and after retirement likely be higher or lower than that of the S&P 500, and why? (Assume effectively zero management expense fees (you can now do this with one of Fidelity's mutual funds) with this extreme low-cost indexed mutual fund and ignore taxes)