Congratulations! Today is your 20th birthday is today, and you just started work
ID: 2774149 • Letter: C
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.