A Little IRA Math

By Brad Thomason, CPA


Did you do it too?  You know, sit there in math class at some point as a kid and utter that proverbial interrogatory, “When am I ever gonna use this stuff in real life?!?!”  Well…

Today’s lesson, class, is about the commutative property of multiplication, wherein we remind ourselves that:

A x B x C = C x A x B = B x C x A, etc.

With April 15th fast approaching, and taxes on every one’s minds, today seemed like a good time to make a few comments about one of the financial industry’s favorite tax-related topics, the Roth IRA.

Consider the following 2 cases:

Mr. X earns $30,000 over a period of years.  He puts it in an IRA where it triples in value over time.  He withdraws it as a lump sum, and pays 33% in taxes.  He is left with $60,000 in cash.

Now, the second case:

Mr. X earns $30,000 over a period of years.  He pays taxes at the rate of 33% and then puts the money into a Roth IRA.  Over a period of time the balance triples.  At the end he is left with $60,000 in after-tax cash.

Note that the results are the same.  Does that surprise you?

The way the financial industry bills Roth IRAs you could certainly draw the conclusion that they are derived from pure, elemental magic.  The fact that you don’t have to pay taxes on whatever you earn seems too good to be true, like the government left a gate open, through which you actually could escape the inevitability of taxes.

No they didn’t.  You already paid the taxes.

Consider the math:  you multiply some amount of money by some factor that represents investment performance by some percentage for taxes.  Three variables.  Doesn’t matter what order you multiply them together, the result is the same.  With traditional IRAs the investments variable is second and the tax piece is last.  For Roths, that order is reversed (you pay the taxes before you start investing).  But either way, the equation kicks out the same answer.

Roth IRAs have been around since 1997, and though they do have some attractive features, the most hyped feature is really no feature at all: converting won’t give you more after-tax money.

But what about all those commercials?

How about a little external confirmation:  The National Underwriter company is a major source of information and publications for the insurance and planning industries.  Every year they publish a number of “field guides” that financial professionals can use as quick references when trying to work through the mechanics of cases.  Here’s a brief passage from their 2001 Field Guide to Estate Planning, Business Planning and Employee Benefits (I picked the 2001 edition to underscore the point that the topic of this article is by no means new news):

“Assuming the same tax rate prior to and after retirement there is no difference between the after-tax distributions from a Roth IRA and a Traditional IRA.”

It goes on to state that those who have lower taxes in retirement years would end up with more money by sticking with a Traditional IRA versus converting to a Roth.

So there you go.

Again, Roths have some important features that make them different, and depending on your situation those features might make them a better fit.  But they do not in and of themselves create the one thing which you are most interested in: more after-tax dollars.

When given a choice, I always like to stick with the math, irrespective of what the folks who write ads for the financial industry think.

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