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## JournalJournal: Is the Roth IRA the biggest fraud ever?1

Let's say that my employer is about to give me \$1000. Let's say that I can either put it into a traditional IRA, a Roth IRA, or a non-tax-deferred account. That gives me three options. What's the best choice for me?

I'm going to assume that I live in a state with no income tax. How your state treats these sort of things will change the numbers a bit, but -- I suspect -- not change the final analysis. I'm a solidly middle-class taxpayer in the 25% tax bracket. So, my choices are to invest \$1000 in my IRA, \$750 in my Roth IRA, or \$750 in my regular investment account.

Let's assume that all three accounts have the same underlying investment options, and that no matter where I put it, it's going to get the exact same growth every year.

The question to ask now is, which choice is best? If I'm going to hold the account until retirement, which choice will give me the most money? On the other hand, what if my situation changes and I need money 1, 5, 10, or 20 years from now?

In the formulas below:

I = Initial deposit

g(x) = What \$1 would have grown to after x years

T5 = 1 - Tax rate in 2005 (75%)

TW = 1 - My marginal tax rate at the time of withdrawal

"retirement" = age 59.5

p = profit; equal to (opening deposit) * g(x) - (opening deposit)

Money put into a IRA can not be withdrawn without penalty. So, if I put my \$1000 in, I have to pay the 25% marignal tax rate to withdraw it, plus an additional 10% penalty. While the \$1000 will grow as long as it's in there, I'll only get 65% of any dollar I take out before retirement and 75% of each dollar afterwards. So, until I retire, the amount of money I can withdraw from the account is (I * g(x) * (TW + 10%)). After I retire, the 10% part goes away, and the total amount of cash I can pull out of the account is (I * g(x) * TW)

Money has to be taxed before I can put it into a non-deferred account. So, starting with \$1000, I can't put more than \$750 into my non-deferred account. However, I can withdraw it without additional penalty. If I invest it in a long-term capital-gains-generating investment, then after a year, the profits are only taxed at 15%. That means that the total withdrawable cash from this account is (I * T5) + (p * .85). This formula does not change at retirement.

Finally, I could put it into a Roth IRA. Money must be taxed before going into a Roth IRA, so again, the maximum I can put in is \$750. However, it combines a few features of the regular IRA and the non-deferred account. Money put in can be taken out without penalty, so I could withdraw that \$750 immediately without penalty. The profit can be withdrawn after only 5 years and treated as normal income; before that, there's an additional 10% surcharge. Finally, once you hit 59.5, *all* of the money can be withdrawn completely tax-free, without giving a single dime to Uncle Sam. In the first five years, the withdrawable value of a Roth IRA is (I * T5 + (p * (1 - TW - .10)). After five years, that .10 disappears. At retirement, the TW becomes 0, and so the final, withdrawable balance of a Roth IRA becomes simply (I * T5 * g(x))

That's where it becomes interesting. Look back a couple of paragraphs to see what the final withdrawable balance of a traditional IRA is. It's (I * g(x) * TW). That's nearly the same formula, the only difference is that with a traditional IRA, you pay the marginal tax rate at retirement, and with a Roth, you pay the marignal tax rate at contribution time. The fact that the Roth grows and can be withdrawn tax-free is exactly cancelled by the fact you have to pay the taxes up front instead of at the end. If the tax rates are the same at both times, then the two accounts will have exactly the same withdrawable balance.

So, the difference after retirement between a Roth and a regular IRA is exactly equal to the difference in tax rates at deposit and withdrawal time. There is one other major advantange of a Roth once you hit retirement -- you can withdraw the entire thing in one lump sum without tax consequences. If you try to pull hundreds of thousands of dollars from your traditional IRA upon hitting 59.5 years old, you'll push yourself into an even higher tax bracket.

As I write this, I'm more than 30 years away from turning 59.5. While I contribute to tax-deferred accounts, I don't know for sure that I'll never suddenly decide that I want to access that money. Which account is best if I want to access my money before I hit 59.5? Let's assume that I go at least 5 years, so that the 10% penalty on the Roth goes away, and the non-deferred account is in the 15% tax bracket.

The first answer that springs to mind is the non-deferred account. There are no penalties on early withdrawal and it's taxed at a lower rate than either of the other two. If, after five years I want to empty my account, the withdrawable value will be:

Non-deferred: (I * T5 * g(x)) - (p * .15)

Roth: (I * T5 * g(x)) - (p * (1 - TW))

Trad. IRA: (I * g(x) * (TW - .10))

Because the relationship between these formulas is non-obvious, let's plug in some hard numbers and see what happens.

I = \$1000

T5 = .75

g(x) = {1, 1.5, 2, 3, 4, 5, 6}

TW = .75

(Sorry, please ignore the spaces and dots. A working way to insert pre-formatted text would be nice...)

.........1......1.5.......2.........3.........4........5 .......6

N-D....\$750....\$1067.....\$1388.....\$2025....\$2663 ....\$3300....\$3938

Roth...\$750....\$1313.....\$1238.....\$1875....\$2438 ....\$3000....\$3563

T.IRA..\$650.....\$975.....\$1300.....\$1950....\$2600.... \$3250....\$3900

As you can see, if g(x) is low, the non-deferred account is best. However, as g(x) gets larger, the traditional IRA, because there's more capital there to grow, has its withdrawable balance approach that of the non-deferred account. In fact, they cross at g(x) = 9, though I'm not sure why.

The Roth IRA will have a higher withdrawable balance than the traditional IRA, but only as long as g(x) < 1.62. That's close to, but not equal to the golden ratio.

Something else to note is that contribution and withdrawal rules for company-sponsored 401(k) plans are almost identical to those of traditional IRAs.

So, in conclusion, if I'm going to have any chance of needing to access my money before retirement, a non-deferred account is probably best, unless I'm pretty sure that my money will have grown by ~10x or more by then. However, if I'm going to be accessing my money after retirement, it's absolutely irrelevant to me whether I put my money into a Roth or a traditional IRA.

That ignores the fact that contribution limits are higher for Roths than traditional IRAs; there are people who can put money into a Roth who can't put money into a traditional IRA.

So, as a taxpayer, it's irrelevant. Does it matter from a public policy perspective?

If I put \$1000 into a traditional IRA, there's \$1000 out there in the economy, growing, funding businesses, being loaned to homeowners, and so on. However, if I put it in my Roth, only \$750 goes out and does that. The other \$250 goes straight to the government, to be spent on foreign wars, chocolate-covered performance artists, and the like.

In a world where IRAs are the preferred savings vehicle, the government basically allows citizens to invest money that would otherwise have been given up in taxes. In return, the government will collect that same money with not just interest, but market rates of return, but without all of the problems that happen when the government tries directly owning businesses.

On the other hand, the Roth IRA is a way to collect that tax money immediately, in return for giving up taxes on future profits from it.

In other words, when the government created Roth IRAs in 1998, it essentially cashed out its long-term savings. This resulted in a short-term increase in govermnent revenue, followed by a longer-term stagnation in the economy as there was less and less money available to drive it.

It's not hard to admit errors that are [only] cosmetically wrong. -- J.K. Galbraith

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