Question

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 $5 million by your 60th 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.

Required:
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, 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%. 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)?

Answer 1

A) $790.63

B) $718.75

C) $503.13

Step-by-step explanation:

a. Interest rate = 10%, monthly rate = 10%/12 = 0.10/12

Number of years = 60-20 = 40 years = 40*12 = 480 months

Goal = FV = 5,000,000

The monthly savings needed if employers offers no match =PMT(rate,nper,pv,fv) =PMT(0.10/12,480,0,5000000)

= $790.63

b. If employer offers a 10% match.

Then monthly savings needed

= 790.63/1.10

= 718.75

Monthly savings needed with 10% match by employer

= $718.75

c. Tax savings are 24%+6% = 30%.

So on the contribution of 718.75, you save a 30% tax. So. tax savings = 718.75*0.30 = $ 215.63

So, monthly contribution taking into account tax savings and employer match

= 718.75 -215.62

= $503.13