Congratulations! Today is your 21st birthday. You just started working full-time
ID: 2475794 • Letter: C
Question
Congratulations! Today is your 21st birthday. You just started working full-time, earning $100,000 per year. Your goal is to have $5 million in your 401(k) plan by your 61st birthday (i.e., 40 years from today). Assume 3% inflation per year. If you can earn 10% per year annualized in an S&P 500 mutual fund, after all expenses, inside a 401(k) with a dollar for dollar match up to 10% of your income, how much would you need to save each month to have that $5 million:
(a) If that $5 million is in future nominal dollars;
(b) If that $5 million is in today’s equivalent purchasing power future dollars;
(c) If your marginal tax rate is 34% federal plus 7% state, what would the after-tax cost of your investments be for (i) and (ii) if you relied on the employer match for ½ of your monthly contributions?
(d) In retirement, you plan to draw $10,000 per month of principal from your investments. If you were 100% invested in stock mutual funds (like the S&P 500), would you get more or less than the rate of return on the S&P 500 - and why?
Explanation / Answer
f we save $x per month, then the 401(K) will have $2x per month, and $24x put into it per year, up to a maximum saving of $10,000 per year. This money will grow at 10% per year or 10/12 % per month in nominal dollars. If we take into consideration inflation, this money will grow at 10 - 3 = 7% per year and 7/12 % per month.
Since we are depositing money on a monthly basis, we must use a month as the time period. Since we have 40 years, we will have 40*12 = 480 months
Now, we can answer the questions:
a) We expect 5 million in nominal dollars, hence we calculate the value of annuity payments
PMT of Annuity (PV = 0, FV = 5000000, rate = 10/12 %, periods = 480)
From excel or a financial calculator we get payment = $790.63
However, since the 401k matches 1 for 1, you need to save only half of that, which is extbf{$395.31}
b) we do the exact same thing as part a) but we use the rate of 7/12% as we had calculated before
Hence PMT of Annuity (PV = 0, FV = 5000000, rate = 7/12 %, periods = 480)
From excel or a financial calculator we get payment = $1904.90
Half of that is $952.45. However, the dollar for dollar match is only for 10% of income. This means $10,000 on a yearly basis and 10,000/12 = 833.33 on a monthly basis.
Hence, to get the amount that needs to be saved we do 1904.90 - 833.33 = extbf{$1071.56}
c) Marginal Tax Rate = 41%
d) In retirement, withdrawing 10,000 per month would give you a return of lower than the S&P 500 because you will have to pay out taxes when you withdraw, and you will be generating return on a smaller principal as compared to if you were 100% invested in stock mutual funds.