Roth vs Traditional Investing assuming same tax bracket in retirement

I've done a little (simplified) math to determine the difference in investing in a Roth account and a Traditional retirement account.

I'm assuming that I will be in the same tax bracket in retirement as I am now -- 15%.

Here's what I've come up with:

``````Pre-tax amount:
100 * 1.0 = 100

Maturing at 8% for 30 years:
100 * (1.08 ^ 30) = 1006.27

Amount taxed at 15%:
1006.27 * 0.85 = 855.33
``````

Roth Investment:

``````Post-tax amount:
100 * 0.85 = 85

Maturing at 8% for 30 years:
85 * (1.08 ^ 30) = 855.33

Amount not taxed:
855.33 * 1.0 = 855.33
``````

Assuming my math is correct and that I'm not missing something about Roth investments, it appears to me that either option will work out exactly the same if you will be in the same tax bracket in retirement.

Question:

Is investing in a Roth retirement account only better if you will be in a higher tax bracket in retirement?

If so, is there any case in which a traditional retirement account is better than a roth account?

• I think @JoeTaxpayer had a blog post about doing both, somewhere
– Noah
Aug 26, 2014 at 18:10
• I think if you expect to be in a lower tax bracket during retirement, then you will find the traditional account to be better. Aug 26, 2014 at 18:27
• For what it's worth, most of my 401(k) is traditional because that's what was available when I started it. About a decade ago I switched new deposits to go in as Roth for no good reason at all beyond a certain sense of "if I don't know which way to bet, I can always diversify". At some point I'll talk with a financial advisor about whether I want to change it again to split new deposits between the two modes, and if so how. Aug 26, 2014 at 19:26
• @Noah I found this article by JoeTaxpayer on the subject. It's a good read. Aug 26, 2014 at 20:45
• @VBCPP: Withdrawals are also from the top. It's just that withdrawals tend to take a large percentage of the income, so it is likely to drop down into lower brackets too. Whereas contributions are made with a tiny percentage of the income, so is likely to be entirely within the top bracket. Aug 27, 2014 at 7:07

Broadly speaking, a traditional account is better if you will be in a lower tax bracket in retirement (see for instance here). When you put the money in now, you pay no taxes on it at your current (high) rate; when you take it out, you will pay taxes at your future (low) rate. You push the taxes onto your future, lower-rate self.

This is, crucially, assuming you can deduct the contribution on the traditional IRA. If you can't (e.g., because you have an employer-sponsored plan and make too much money), the traditional IRA doesn't really gain you anything (see here).

That is the basic story, but there are some other differences to consider as well. For instance, if your income is too high, you cannot contribute to a Roth at all. Also, with a traditional IRA you're required to start taking money out at a certain age, whereas with a Roth you never have to; this can make a difference if you have other retirement income and want to leave the money in the Roth (e.g., to pass on to your heirs without having to pay an intermediate tax at withdrawal).

On a more speculative level, there is the possibility that tax rates may change between now and your retirement; some people try to hedge against this possibility by strategically allocating their retirement assets based on whether they think tax rates will rise or fall.

• This answer covers the basics, but it's also worth noting the inherent uncertainty with tax rates. Personal income taxes in the United States are quite low relative to its own history and to the rest of the world. Looking at the amount of debt we have, it's reasonable to assume those low rates can't/won't continue indefinitely. So in some cases it may make sense to pay taxes now even if hypothetically, your rate could be slightly lower in retirement. Aug 26, 2014 at 18:40
• @CraigW: I had something about that in there but took it out before posting. I added it in now. I agree it is something that people do, but I think speculation about future tax rates is in a different category of possible factors, since unlike your individual income and retirement goals, future tax rates are almost totally out of your control. Aug 26, 2014 at 19:00
• +1 for changing tax rates. If you're young, the chances that the tax rate will change by the time you retire are pretty darn high. =) Aug 26, 2014 at 22:14
• Tax rates may change, but there's also a non-trivial chance of the rules changing. How secure do you feel about betting that the Roth tax haven won't be eliminated, and the earnings subjected to taxation? Aug 27, 2014 at 7:28

Is investing in a Roth retirement account only better if you will be in a higher tax bracket in retirement?

If you are pushing up against the contribution limits, a Roth account may allow you to save more money in tax-advantaged accounts. In your example, you are putting \$100 pre-tax in a traditional account vs \$85 post-tax in a Roth account. But if there are limits, and the limits are the same for traditional or Roth accounts (as they currently are for US 401(k) accounts), you can effectively put more into a Roth account, where the limit applies to the post-tax amount, than a traditional account, where the limit applies to the pre-tax amount.

If so, is there any case in which a traditional retirement account is better than a Roth account?

It is smart to have some money in a traditional account, because the first amount of money you earn or withdraw each year (up to the standard deduction) is taxed at 0%, which is probably less than your current rate. And the next bit of money is taxed at only 10%, which may also be less than your current marginal rate. Of course, things may change by the time you retire, but it is probably safe to assume that we will still have some kind of progressive (income bracketed) tax structure.

Assuming my math is correct and that I'm not missing something about Roth investments, it appears to me that either option will work out exactly the same if you will be in the same tax bracket in retirement.

This is true only if your average tax rate in retirement is the same as your current marginal rate. I'm surprised none of the answers mention this since it is the crux of your question!

If you can deduct an IRA against your income taxes, it is almost always better option than the Roth equivalent. Marginal rates should not be compared to average rates or you will form all sorts of inaccurate conclusions.

"If you are in a lower tax rate in retirement traditional is better" really means, "if your average tax rate in retirement is lower than your current marginal rate, traditional is better" - which for the overwhelming majority of Americans is the case.

Example

Consider the following. Let's say your intend to contribute \$1000 in one year (making \$2k) and withdraw it the next that is your only income in that year. Your tax brackets look like:

• First \$500 income, 0%
• Everything above \$500, 15%

This is quite simplified but for this purpose will illustrate precisely why comparisons like you are making are very misleading.

In this case you can put \$1000 in and pay no income tax at all (because you deduct it). You then withdraw \$1000 the next year. The first \$500 you withdraw you pay no taxes on and the next \$500 has a tax rate of 15%, for a total tax of of \$75.

However - this is a tax against your entire withdrawal of \$1000, so your average tax rate (this is important! average is different than marginal) is only 7.5% and you are left with \$925.

Roth IRA

In this case you can only contribute \$850 to the IRA because you are taxed against the money at your marginal rate (15%).

When you withdraw it, you don't pay any taxes and are left with the entire \$850 \$850. This is less than the above, because you are taxed the whole amount at your previous marginal rate.

If however your tax rate in retirement was 30% for everything above \$500, only then are the two scenarios equal. Your marginal tax rate in retirement has to be very high relative to your current tax rate for the Roth to ever catch up and be better.

So what?

If you are able to deduct an IRA contribution, it will almost always be the best option. The average federal income tax rate on middle class families has not changed dramatically enough over the past 50 years to be above normal marginal tax rates - even at the 15% federal tax bracket, your marginal rate is still higher than the highest average tax rate for the past 50 years by at least 3% and normally significantly so.

The reason I make this point about middle class marginal rates is that the majority of "taxes might be higher in retirement!" is very unlikely to be the case in a meaningful way given the past 50 years. However if you are in the top tax rate you are paying historic low tax rates (by a factor of nearly 3), but also observe you can't do either IRA since you must make \$400k/year. The difference for middle class is no where near as noticeable.

Keep in mind if you can't deduct, there is no reason to not contribute to the Roth.

• Also note this is true for Roth/traditional 401k decisions, as well. Aug 28, 2014 at 1:07
• It's not "average tax rate". It's only "average tax rate" for the portion of the income that is from the Traditional withdrawal. You are assuming that this constitutes all your income in retirement. (Similarly, you can also say that when you contribute for Roth, the money that was contributed was also taxed at "the average rate" -- the average rate for the portion of income that constituted the contribution.) Aug 28, 2014 at 5:59

Luke, I'd like to point out some additional benefits of the Roth IRA accounts

1) Going Roth, you can effectively increase the amount of your contribution to your IRA account. In your example, you are assuming that your contribution to Roth IRA is in fact \$ 85 (\$100 less \$ 15 tax paid). In reality, albeit more costly, Roth IRA allows you to contribute full \$ 100 (\$117.65 less \$ 17.65 tax incurred.) Using this method you can in fact grow your tax-free funds to \$ 1.006.27 over 30 years. The larger you effective tax rate is, the larger will be the difference between your maximum effective Traditional vs Roth IRA contribution will be.

2) Should you need to access your IRA funds in case of emergency (unqualified event of not buying your first home, nor paying for your college education), Roth IRA account contributions can be withdrawn without incurring the 10% penalty charge, that would be imposed on your unqualified Traditional IRA distribution.

3) As other contributors noted it's hard to believe that lower US tax rates would prevail. Chances are you will be contributing to Traditional 401k later throughout your work life. Having a Roth IRA account would afford you a tax diversification needed to hedge against possible tax rate hikes coming in the future. Considering the gloomy future of the Social Security funding, and ever-growing US national debt, can we really expect for there to not be any tax rate increases in the next 20-40 years?! By the way, as others pointed out your effective tax rate will always be lower than your marginal tax bracket.

Yes your basic math is correct. If your tax bracket never changes, then either type of retirement account will end up in the same place. Assuming that there are no income restrictions that will limit your ability to contribute to the type of account you want.

Now your job is to guess what your tax bracket will be each and every year for the next 3 or 4 decades. Events that will influence your bracket: getting married; having children; buying a house; selling a house; paying for college; the cost of medical care; moving to a state with a different state tax structure. Of course that assumes that you don't get a big bonus one year or that congress changes the tax brackets.

That is why many people have both types of retirement accounts: Roth and non-Roth.

Your math is correct. If you take the same amount of pre-tax wages (assuming that that amount can be fully contributed in both Traditional and Roth cases), and assuming the same flat tax rate when contributing and withdrawing, then the two are the same.

However, we don't have a flat tax, and due to the way our tax brackets work, there is often a slight advantage to Traditional accounts. Recall that not every dollar of your income is taxed at the same rate; the tax bracket only describes the rate that the last dollar of your income is taxed at. But some of your income will be taxed at lower brackets. No matter what your income is, your first \$x of income will be taxed at 10%, then \$y at 15%, etc.

So what is the tax rate of the dollars of income that you used to contribute to a retirement account? Is it the first dollars of income? The last dollars of income? or what? Since we are comparing an after-tax contribution (Roth) versus a pre-tax contribution (Traditional) whose income doesn't show up in taxable income, and all other income is equal, the dollars contributed is considered to come from the top in the Roth case. Similarly, when you withdraw in the Traditional case, the withdrawal counts as income; is it the first dollar of income or the last dollar of income? Again, since we are comparing the situation where the withdrawal counts as income (Traditional) with the one where it doesn't (Roth), all other income being equal, the taxable income is considered to be added to the top.

The difference is that when you contribute to a retirement account, you contribute a very small percentage of your income every year, probably no more than 5-10%. If we count down from the top, this small percentage of your income probably falls wholly within a bracket (in other words, the taxable income in Traditional and Roth cases are likely in the same bracket), so the entire contribution is at the same rate -- your marginal rate, the rate you cite as your tax bracket.

However, when you withdraw in retirement, it is likely that every year, the retirement account withdrawals account for a large percentage of your income, maybe even half or more. If we count down from the top, this large percentage of your income probably crosses into lower brackets (in other words, the taxable income in Traditional and Roth cases are likely to be in different brackets), so the withdrawal is partly taxed at one rate, partly taxed at another. So if your tax bracket is 15% in the Traditional case, it's likely that your withdrawal is taxed partly at 15% and partly at 10%. So in this case, the average tax rate on the withdrawal is lower than your "bracket".

The assumption of "same tax bracket in retirement" is convenient, but simplistic.

If you are in, for instance, the second-lowest bracket now, and happen to remain in the second-lowest bracket for retirement, then Roth and traditional account options may seem equal — and your math backs that up, on the surface — but that's making an implicit assumption that tax rates will be constant. Yet, tax brackets and rates can change. And they do. The proof.

i.e. Your "15% bracket" could become, say, the "17% bracket" (or, perhaps, the "13% bracket") All the while you might remain in the second-lowest bracket.

So, given the potential for fluctuating tax rates, it's easy to see that there can be a case where a traditional tax-deferred account can yield more after-tax income than a Roth post-tax account, even if you remain in the same bracket: When your tax bracket's tax rate declines.

So, don't just consider what bracket you expect to be in. Consider also whether you expect tax rates to go up, down, or remain the same. For twenty-something young folk, retirement is a long way away (~40 years) and I think in that time frame it is far more likely that the tax brackets won't have the same underlying tax rates that they have now.

Of course, we can't know for sure which direction tax rates will head in, but an educated guess can help. Is your government deep in debt, or flush with extra cash? On the other hand, if you don't feel comfortable making predictions, much better than simply assuming "brackets and rates will stay the same as now, so it doesn't matter" is to instead hedge your bets: save some of your retirement money in a Roth-style account, and some in a traditional pre-tax account. Consider it tax diversification.

I think others have made the key points. Let me just add:

As others have pointed out, the traditional IRA is better if your tax rate in retirement is lower than it is when you are building the account. The Roth IRA is better if your tax rate in retirement is higher.

For most people, your income in retirement will be lower than your income in most of your working years. On top of that, a significant percentage of your income will come from Social Security, which is generally not taxed, and so the tax rate you pay on the remaining income will be lower still.

If you're just starting out, if you're in your 20s, it's likely that your income will go up significantly in the next couple of decades and so you might be making more in retirement that you are now, and so the Roth is probably your better bet. But if you're in your 40s or 50s you are probably making your peak income, you will have much less in retirement, and the traditional IRA is likely better.

If your income is well above average and you are saving enough to have a retirement income well above average, then social security may be a very small part of your retirement and my comments on that may not be relevant to you.

It's true that tax rates could change in the future. But will they go up or down? It's also possible that the laws about retirement accounts will change. If you think you have some insight into what will happen in the future you may want to take that into account when making plans. But politics is very hard to predict.

One additional benefit of a Roth IRA in addition to the others mentioned above is that if you need to withdraw a lot of money in one year during retirement (let's say to buy a 2nd home), you can withdraw from both the Roth IRA and traditional IRA. That way, you can avoid the high tax brackets since you won't need to take as much out from your traditional IRA.

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its important to reiterate that his assumption is correct. ... if the tax rate doesnt change... you have zero extra benefit (mathmatically) to compound pre tax money in a traditonal IRA and then paying tax only when you later withdraw VERSUS paying tax now (ROTH) and letting it compound tax free and withdraw tax free later. most people are confused by this because they are shown by 401k planners how much that 'pre tax money grows while compounding' but in the end , its mathmatically equivalent. I can easily imagine many professional high wage earners being in a higher tax bracket in retirement than they are now , especailly looking at our huge debt and political leanings towards socialist type candidates