Congratulations! Today is your 20th birthday is today, and you just started work

Question

Congratulations! Today is your 20th birthday is today, 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. 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; and (c) what will dollar cost averaging do to your investment, and why?

Explanation / Answer

(a) At nominal rate,

Monthly savings = Future value * (Annualized rate/12) / [(1+Annualized rate/12)No. of months - 1]

= $1,000,000 * (11%/12) /.[(1+11%/12)35*12 - 1]

= $202.91

(b) At equivalent purchasing power,

Discounting rate = Nominal rate - Inflation rate

= 11% - 3%

= 8%

Monthly savings = Future value * (Annualized rate/12) / [(1+Annualized rate/12)No. of months - 1]

= $1,000,000 * (8%/12) /.[(1+8%/12)35*12 - 1]

= $435.94

(c) Dollar cost averaging means fixed dollar investment wherein more shares are purchased when prices are low and less shares are purchased when prices go down.

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