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Author: Lemuel Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: of 121061  
Subject: Roth versus Traditional IRA Date: 1/31/1998 2:36 PM
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To TMFTax:
In your recent article discussing the option of Roth or Traditional IRA, you concluded by saying that the fictional Sarah should probably choose the Roth IRA. I was confused by this.
In advising my parents about the Roth IRA, I discovered that basically the Roth comes down to a simple property of multiplication, the associative property.
The basic future value formula for an investment is as follows:
([Principal]*(1+[Interest Rate])^[Number of Periods])
The Roth IRA takes its tax rate at the beginning, multiplying by the principal. The Traditional IRA takes its tax rate at the end, multiplying by the whole thing. But it really doesn't matter if the tax rate is the same. However, we all usually expect the tax rate to be different. We expect it to be less at the end. So that, I believe, makes the Traditional IRA more attractive for most people. The Roth, though, does have some attractive features, like the lack of penalty for withdrawal of principal or the educational clauses, etc.
Let's take Sarah as our example. I'll restate some of the facts for people that haven't read the original article.
Sarah is 30 and makes annual contributions of $2000. She's looking to maximize her balance after taxes when she turns sixty. She earns 10% a year. She's apparently going to make a contribution in the year she turns 30 and take a lump sum distribution the year she turns 60 without making a contribution in that year.
Right now Sarah's in the 28% bracket and when she retires and then takes this distribution at 60 she expects to be in the 15% bracket.
When Sarah turns 60, she checks her balance on the Traditional IRA and it's $361,886.85. She owes taxes on this at 15% and has $307,603.82 left ($54,283.03 in taxes).
However, if Sarah chose the Roth IRA, she'd check her balance at 60 and see $260,558.53. Remember, she was in the 28% bracket when she was making these contributions. She paid $560 of each of her $2,000 payments to the IRS. Each effective contribution was $1,440. Yes, the total dollar amount of that contribution was only $16,800. However, taking into account the time value of money, (Ben Franklin once said: “One today is worth two tomorrows.”), this $16,800 ballooned into $101,328.32 at 10%.
The Traditional IRA, to me, looks like a better choice. But are we comparing apples to apples? What if Sarah is not limited to just $2,000 for investment? She could invest, say, $2,777.78 before taxes and make that $2,000 max Roth IRA contribution (28% of $2,777.78 is $777.78). I would suppose this is okay, but I have not read these laws for myself. But let's say it's true just in case.
Now with the Traditional IRA, Sarah invests $2,000 of her $2,777.78 in the IRA. The other $777.78 is taxed at 28% and thus reduced to $560. Every year she pays a tax of 28% on her earnings on this money and so earns an aftertax return of 7.2%.
When Sarah turns 60, her $2,000 Roth IRA has become $361,886.85. Hey! No taxes!
Now with the Traditional IRA option, Sarah turns 60 with her IRA at $361,886.85 and pays taxes at 15% now reducing her IRA to $307,603.82. But remember that additional $777.78 a year that's really reduced to $560 a year at 7.2% after taxes? That's now worth $58,788.70. So the total Traditional IRA wins at a total of $366,392.52. It doesn't win by much in this scenario, so if this is legal and you've got plenty of money laying around for these reduced-tax vehicles, then you'd probably want to weight the benefits of the Roth.
Please post responses to this analysis. I'd really like to hear thoughts about it.

-Lemuel, whose wisdom, however much or little he's been granted, is all from God.
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