Today is your 20th birthday, and you just started working full-time, earning $50

Question

Today is your 20th birthday, and you just started working full-time, earning $50,000 per year. Your goal is to have $1 million by your 55th birthday (i.e., 35 years from today). Assume 3% inflation per year, and a marginal federal plus state income tax rate of 32%. if you can earn 11% per year annualized in an S&P 500 mutual fund, after all expenses, inside a Roth IRA, how much would you need to save each month to have that $1 million if:

a) that $1 million is in future nominal dollars; or

b) if that $1 million is in today's equivalent purchasing power future dollars;

c) whay will dollar cost averaging do to your investment? why?

d) what is the after tax monthly cost of your investment?

Explanation / Answer

a)Annual compounding Rate= 11%*1.03*(1-0.32)= 11%*1.03*0.68= 0.077044 Future value @ end of 35 Yrs.=1000000 Using the future value of annuity formula 1000000=PMT*(1.077044^35-1)/0.077044 PMT=Annual savings each month= 6196.77 b) PV of Future $ = 1000000 Using the present value of annuity formula 1000000=PMT*(1-1.077044^-35)/0.077044 PMT=Annual savings each month= 83240.8

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