This is a question I hope a LOT of people are asking.  I hope everyone out there has been thinking and researching about the road to retirement to come to this fork.  The most common advice I’ve heard is simple:

If you think you’ll be in a higher tax bracket in retirement, choose Roth IRA (or Roth 401k).  Otherwise, choose an IRA (or 401k).  But as a quantitative tech guy, I want to provide a little more detail.  I don’t like a lot of online calculators that just tell you what to do but don’t go into how they made their calculations.  So I made this Google spreadsheet.  Best way to play with it and copy all the cells onto your own Spreadsheet program.

Let’s take a closer look

The spreadsheet assumes you receive a one-time “paycheck” of $1,000 and tracks how much it grows after 30 years in either the Roth and Traditional accounts.  Although in real life you would contribute to your retirement account monthly, for this illustration I assume just a 1 time paycheck.   There are 3 variable inputs:

  1. Tax rate today
  2. Tax rate at retirement
  3. Annual rate of return of investment

Since there’s only 1 cell for for each of the tax rate, you’ll need to put a percentage that includes federal, state, and local taxes.  For annual rate of return, you can put an estimate based on the type of investment you would put put the money in.  If you like, you can reduce this amount by 3% to adjust for inflation.  So if you assume you would put it in an S&P 500 index fund that returns 10% annual rate of return, you might enter 7% just to adjust for inflation.

There are 4 outputs:

  1. Roth total:  Total amount after 30 years if invested in a Roth IRA/401k
  2. Traditional total:  Total amount after 30 years if invested in a traditional IRA/401k
  3. Traditional total – Roth total:  A positive amount means it was better to invest in traditional
  4. (Traditional – Roth)/Traditional

 

Case Studies

Case 1: Equal tax rates now and at retirement

The trivial case is if you think you’ll be at the same tax bracket now and at retirement. In this case, perhaps not surprisingly, you end up with the same total after 30 years in both types of retirement accounts. That doesn’t mean it doesn’t matter which type you choose. They both have pros and cons outside of tax accounting. For example, in a Roth IRA, you can take out the principal (but NOT the earnings) penalty-free and tax-free (since it’s already taxed) any time. This helps in emergency situations. For a traditional 401k, you can take a loan from it. When you do this, interestingly, you have to pay “interest” on your loan but since it’s a loan from yourself to yourself, the interest you pay goes back into your traditional 401k. I won’t go into any more details on this post, but you should look into the other pros and cons.

Case 2: Tax rate today is 28% and retirement is 15%

Maybe you figure your retirement tax rate will be much less. Perhaps you plan on living more frugally or moving to a state without any state income tax (ever wondered by so many people move to Florida to retire?). In any case, if you made this assumption you’d be ahead $535 if you chose Traditional over Roth.  To see why, take a look at the other cells in the spreadsheet.  Start with row1:

Year Roth Traditional
1 $720 $1,000

Under the Roth account, at year 1 you would be taxed at 28%, leaving you with $720 ($1,000 – $280). Of course under the traditional account you get the full $1,000 since it starts tax free. For years 2-30, for both accounts, your money compounds yearly at the specified annual rate of return. For each year, this is accounted simply by taking the previous year and multiplying it by (1 + annual rate of return). After 30 years, this gives:

Year Roth Traditional
30 $2,964 $4,116

Then, of course, for the Traditional account Uncle Sam finally gets paid. So while the Roth total is unchanged (remember you paid taxes on it in year 1), the traditional total goes down to $3,499 ($4116 – $4116 * 15%)

Roth Total $2,964
Trad Total $3,499

Thus, in this case you’re better off using the traditional IRA/401k, by $535.

Case 3: Tax rate today is 15% and retirement is 28%

In this case, you can use the spreadsheet to double check but it turns out you’d be better off with the Roth IRA/401k by the same $535. So the situation reverses. This might be your case if, say, you’re currently a graduate student researcher getting paid near minimum wage while working towards your PhD. Then you would be in a very low tax bracket today and expect to be in a higher one at retirement.

Wrap-up

Hopefully, after looking through the cases and playing around with the spreadsheet you can convince yourself that it’s just simple math the leads to the general advice of “if you think you’ll be in a lower tax bracket at retirement, choose the traditional account.” Note that things are always a bit more complicated in real life. Maybe your company does traditional 401K matching (making the traditional 401k route more attractive), or you just really like the idea of being able to withdraw principal (making the Roth IRA route seem more attractive). The normal blog would tell you “consult with your financial advisor and tax lawyer” but I’ll just say first use your Google and math skills to make sense of it all yourself. If you still can’t figure it out, maybe due to a complicated tax situation, then maybe pay for some professional help. Just keep in mind one truth: nobody cares about your money more than you!