Is a Roth IRA preferable to a Traditional IRA?

This seems like a huge advantage for a Roth to the point where I can't figure out why anyone would choose a traditional.

You are missing something called the time value of money. This is the concept that a certain amount of money now has the same value as a bigger amount of money later. Basically, you wouldn't be willing to give up an amount of money now and get the same amount of money later -- you need to get a larger amount later to be willing to exchange it for a certain amount now. So that larger amount later has the same value to you than that smaller amount now. This is the idea behind interest and investment returns.

When you make an investment, and it earns interest or gains over a period of time, in effect that final amount of money (principal + interest) has the same value as the principal when you started, because that final amount was grown from the original principal.

So whether you are taxed on the principal in the beginning (as in Roth IRA) or on the principal + interest at the end (as in Traditional IRA), you are still taxed on the same value of money. And if the tax rates are the same between now and in the future, then you pay the same value in taxes in both cases. Roth would only be better than Traditional if the tax rates are lower now than when you take it out; and Traditional would only be better than Roth if the tax rates are higher now than when you take it out.

Let's consider a simple example to demonstrate that the two are equivalent if the tax rates (assuming a flat tax, because tax brackets introduce other complications) are the same now and when you take it out. In both cases, you start with $1000 pre-tax wages, you invest it for 10 years in a place with guaranteed 5% returns per year adn then take it out, there are no penalties for withdrawal, and there is a flat 25% tax now and in the future.

• Traditional IRA: You start with $1000 pre-tax and put it in the IRA. It grows for 10 years, to $1000 * 1.05^10 = $1628.89. You are taxed on 25% of it, leaving $1628.89 * 0.75 = $1221.67.
• Roth IRA: You start with $1000 pre-tax. You pay 25% income tax on it, leaving $750 which you put in the IRA. It grows for 10 years, to $750 * 1.05^10 = $1221.67. No taxes are paid when you withdraw it.

Note that you are left with the same amount of money in both cases. This arises from the associativity of multiplication.

Note that Roth IRA has a higher effective "limit" than Traditional IRA, because the nominal limit is the same for both, but Roth is post-tax. So if you contribute to near the limit, where Traditional can no longer match the value that Roth can contribute, then the comparison no longer applies. The $1000 in this example is below the limit for both.

Craig touched on it, but let me expand on the point. Deposits, by definition, are withheld at your marginal rate. And since you can choose Roth vs Traditional right till filing time, you know with certainty the rate you are at each year.

Absent any other retirement income, i.e. no pension, and absent an incredibly major change to our tax code, I know your starting rate, zero. The first $10K or so per person is part of their standard deduction and exemption. For a couple, the next $18k is taxed at 10%, and so on. Let me stop here to expand this important point. This is $38,000 for the couple, and the tax on it is less than $1900. 5%. There is no 5% bracket of course. It's the first $20K with zero tax, and that first $18,000 taxed at 10%. That $38,000 takes nearly $1M in pretax accounts to offer as an annual withdrawal. The 15% bracket starts after this, and applies to the next $57K of withdrawals each year. Over $95K in gross withdrawals of pretax money, and you still aren't in the 25% bracket.

This is why 100% in traditional, or 100% in Roth aren't either ideal. I continue to offer the example I consider more optimizing - using Roth for income that would otherwise be taxed at 15%, but going pretax when you hit 25%. Then at retirement, you withdraw enough traditional to just stay at 10 or 15% and Roth for the rest.

It would be a shame to retire 100% Roth and realize you paid 25% but now have no income to use up those lower brackets.

Oddly, time value of money isn't part of my analysis. It makes no difference. And note, the exact numbers do change a bit each year for inflation. There's a also a good chance the exemptions goes away in favor of a huge increased standard deduction.

One thing people are missing is that you may not be eligible to contribute to a Roth IRA based on your MAGI. There are income "phaseout" ranges which determine how much, if it all you can contribute.

Firstly, eligibility for a Roth contribution phases out above a certain income. If you're above that, you don't have much choice.

Then, if you assume your expenses now are similar to your expenses in retirement, and you'll retire whenever you have enough investment income to cover your expenses, then:

• If your savings rate is low, a Roth IRA is better (but not all Roth, this means you can't take advantage of the low tax brackets after retirement. See JTP's answer.)
• If your savings rate is high, a traditional IRA is better

"Savings rate" means the percentage of your income that goes to your retirement investments.

This seems like a simple conclusion, why is it so?

Paying taxes now is more expensive than paying taxes later.

Say you owe $1000 in taxes on some gains. If you pay them now, you're out $1000. If you can pay them later, you can invest that $1000 and earn a return. When you eventually pay the taxes you still pay $1000, but you keep the returns. This is called the time value of money.

Since puts the Roth at an initial disadvantage: since you pay taxes up front you start with a smaller investment.

On the other hand, a Roth doesn't tax gains at all. This advantage becomes more significant as more of the account value becomes gains and not principal.

For a high savings rate, retirement comes sooner and the fraction of the retirement account that is gains is less, making the traditional IRA better. A low savings rate implies a longer retirement horizon and more account value from gains, making the Roth better.

Income, and thus tax rates, are lower in retirement

As your savings rate increases, it becomes more true that your tax rate will be lower post-retirement.

As an extreme example, consider a married couple with a combined income of $1,000,000 but annual expenses of only $40,000. Their savings rate is a very high 96%, maybe closer to 94% considered on a post-tax basis.

Pre-retirement, such a high income makes their marginal tax rate 37%, using 2020 tax brackets as an example.

However, this couple needs only $40,000 (after tax) to retire. That makes their marginal rate 22%, assuming the brackets don't change. (Of course, that's a rather big assumption, but it will likely be still generally true that less income will be in a lower bracket.)

So this couple could either:

• contribute to a Roth IRA, paying 37% tax (now), or
• contribute to a traditional IRA, paying 22% tax (later)

That's a big difference, and 37% and 22% are just the marginal rates. The effective rates have an even larger spread, since for the low-income post-retirement scenario a higher fraction of income is in the lower tax brackets, and the standard deduction is more significant relative to overall income.

For a high savings rate, this is an advantage for the traditional IRA.

On the other hand, a low savings rate means income will not decrease very much post-retirement, and the tax rates pre- and post-retirement will be similar. The traditional IRA will still have an advantage in this regard, but it will be small.