User:FiveK/Traditional versus Roth

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 refers to the common investment decision of whether to use traditional (pre-tax) or Roth accounts. You must make this decision when your employer offers both a traditional and Roth 401(k), or when you can deduct a traditional IRA contribution or use a Roth IRA, or when you consider leaving money in a traditional account or converting some to Roth.

The better option is the one that gives you (or your heirs, if you are estate planning) more spendable income after all taxes are paid. Preference for one account type or the other is fundamentally a tax planning question.

In a traditional retirement account such as a deductible traditional IRA or traditional 401(k), your contributions are deductible - no tax is paid on account growth while the money remains in the account, and withdrawals are taxed as ordinary income.

In a Roth retirement account such as a Roth IRA or Roth 401(k), your contributions are not deductible, but all future growth and withdrawals are tax-free in retirement.

The approach that incurs a lower marginal tax rate will, in most cases, provide you more spendable income. Neither is inherently better, as either one may be a better choice in different situations. Here are some of the considerations.

General guidelines
See Prioritizing investments for general investment considerations.

The decision between deductible traditional vs. Roth contributions hinges primarily on a comparison between your known marginal tax rate now vs. an estimated marginal tax rate at withdrawal. As discussed in more detail below, estimating future marginal tax rates relies on a lot of assumptions and tax brackets and rules can change at any time.

Assuming you have an estimate for your future marginal tax rate, prefer traditional when your current marginal rate is higher than that estimate, and prefer Roth when your current marginal rate is lower than the estimate.

Those who choose not to estimate future tax rates are left with various rules of thumb for guidance. Because these rules of thumb have many exceptions, a personalized future estimate is recommended, but in lieu of that consider:
 * Contributing 100% traditional, because it's the best choice for most people most of the time
 * Contributing 50% traditional and 50% Roth, because a mix adds tax diversification and you can't be more than 50% wrong
 * Contributing according to some rules of thumb that might be applicable, although most of them still require some assumption about future tax rates.

For those reluctant to contribute at all, either traditional or Roth, or any mix, is almost always a better choice than saving outside retirement accounts. In addition to providing more future income after taxes, traditional and Roth accounts also offer other benefits such as asset protection and estate planning.

Whatever you choose for any one year, you may make a different choice in subsequent years.

Eligibility
Not all investors will be able to choose between traditional and Roth options in all their accounts.

Employer-sponsored accounts (401(k), 403(b), 457(b)) always offer a traditional option, but may or may not offer a Roth option. However, there are no income limitations on contributions, as there are for IRAs.

With IRAs, the eligibility of traditional vs. Roth is affected by income. There is an income limit for deducting contributions to a traditional IRA. Above that limit, and below the Roth IRA contribution income limit, a Roth IRA is best. Above the Roth IRA income contribution limit, one may choose either the backdoor Roth IRA contribution process, a Non-deductible traditional IRA, or a taxable account- see those pages for more details.

See also: Comparison between IRAs and employer plans.

Common misconceptions
There are two common misconceptions, one that incorrectly favors traditional, and one that incorrectly favors Roth.

The first misconception is sometimes described as "contributions are taken from the top tax rate and are withdrawn later at the average rate". In other words, that one saves a marginal rate when contributing but pays only an average rate (starting at 0% for the first dollar withdrawn) when withdrawing. Following is an example of why that is not true.

Consider a 50 year old who has already accumulated a $500K traditional balance. Even without any further contributions, that could reasonably double to $1 million by age 65. Taking a 4%/yr withdrawal then gives $40K/yr. Any traditional contributions at age 51 (or later) will increase the traditional balance at age 65, thus allowing more than $40K/yr withdrawal. The taxation on the amount above $40K/yr will occur at the marginal rate on that amount, not the effective rate on the total income.

The second misconception is that "it's better to pay tax on the seed than the harvest." In other words, that it is better to pay a lesser tax amount now to make a Roth contribution, instead of a larger amount of tax later on a traditional withdrawal. This is not true because taking a percentage of the "seed" is the same as letting the full seed grow and then taking the same percentage of the "harvest." The result will be the same in either case.

The goal should not be to pay as little tax as possible. Instead, the goal should be to have as much money leftover after taxes as possible. Comparing marginal rates between contribution (or conversion now) and withdrawal in the future is the most direct way to achieve this goal.

Calculations
The main reason to prefer one type of account over the other is the difference between current vs. future marginal tax rates.

Simplest situation
For the same pre-tax contribution amount and growth, the after-tax value is entirely determined by the marginal tax rate on contributions and withdrawals. This also applies to "now vs. later" Roth conversions when the tax is paid from converted funds. For Roth conversions, in the discussion below read "traditional" as "convert later" and "Roth" as "convert now".

You can calculate the amount you get after taxes as:

$$ \begin{align} traditional = Original\ amount * Growth\ factor * (1 - withdrawal\ tax\ rate) \\ Roth = Original\ amount * (1 - contribution\ tax\ rate) * Growth\ factor \end{align} $$

The "Growth factor" can be calculated as (1 + r)^t, where r is the annual rate of return and t is the time in years. Because one may choose identical investments in both traditional and Roth accounts, the "Growth factor" is the same for each.

If the marginal tax rate now (the "contribution tax rate") is higher than the marginal tax rate later (the "withdrawal tax rate"), then the traditional account is better; if it is lower, then the Roth account is better. For the Roth conversion decision, "traditional account is better" means "don't convert" and "Roth account is better" means "do convert".

When the withdrawal marginal tax rate will be the same as the marginal tax rate saved by a traditional contribution), thanks to the commutative property of multiplication (i.e., A * B * C = A * C * B) the traditional and Roth results are equal.

More complicated situations
The simple analysis above is valid for many situations, but it does make assumptions that aren't applicable in other situations. Those other situations include

“Traditional plus taxable” vs. Roth
For an apples-to-apples comparison, one sometimes must compare Roth accounts against a combination of traditional and taxable accounts. This situation commonly occurs when contributing more to a Roth than the after-tax amount of the maximum traditional contribution, e.g., when contributing the maximum to their retirement accounts. It can also occur in some Roth conversion decisions; see below for more detail. In these situations, tax drag in the taxable account may make Roth preferable even if the withdrawal tax rate is somewhat below the contribution tax rate.

Niche situations
If you are in either of the situations below, follow the links for details and simple calculations.
 * Investors who are not able to get the maximum employer match
 * Investors eligible for the Saver's Credit on both traditional and Roth contributions

Calculating marginal tax rate now
Your marginal tax rate now is relatively easy to determine. It is not necessarily your tax bracket, because of phase-ins and phase-outs of tax benefits (e.g., business tax considerations, various credits, Taxation of Social Security benefits), and tax-like costs (e.g., Expected Family Contribution, ACA Health Insurance, and IRMAA Medicare premium surcharges); see Marginal tax rate for a more detailed explanation, and Traditional versus Roth examples for examples.

One can use one's favorite Tax estimation tool to calculate the tax change for the maximum contribution or conversion amount considered. If the (change in tax) divided by (change in income) does match one of the nominal tax brackets (e.g., 12%, 22%, 24%, etc.), that is all one need know. If one gets a different answer, more work is needed: using small ($100 or so) changes in income to determine at what point(s) (change in tax) divided by (change in income) gets a new result. This can be done by hand, or using a tool such as the Personal finance toolbox that will provide answers in chart form.

If you can contribute to Roth accounts today at a marginal tax rate of 12% or less, it is usually a good idea. This is a low tax rate historically, and especially if you are far from retirement, many things can change that could cause you to pay a higher rate at withdrawal, such as changes in tax law, moving to a higher-tax state, unexpected increases in income, inheriting an IRA, and others. Only defer taxes at 12% or less if you're close to withdrawal and are very confident you will be able to withdraw at a lower rate.

Estimating future marginal tax rate
Estimating your future marginal tax rate is considerably harder than for today, and high accuracy should not be expected. There are two parts to the estimate: 1) your taxable income, and 2) how tax law will treat that income. While all of these factors have high uncertainty, great precision is usually not needed to make a reasonable estimate.

For tax law, using today's tax rates is generally recognized as a good starting point, but if you have strong feelings that taxes will go up or down in the future, you could make your own adjustments to these numbers.

Your future taxable income will depend on your current situation, and how that situation changes between now and withdrawal.

First, establish a rough baseline plan for how long you will work, how much income you expect to earn, when you expect to retire, and when you expect to begin receiving Social Security and any other guaranteed income. Certain careers are characterized by long periods of low-income training followed by much higher earnings, and these changes should likely be included.

If you're not sure, assuming that your current income continues to a typical retirement age is reasonable. If you think there's a chance your income could drop or disappear, assuming no future income could be reasonable. Estimates for future income should be based off this plan.

To be consistent with using today's tax rates, you should ignore inflation by using real expected rates of return instead of nominal returns for investment growth.

Simple method
Investors who expect most of their future income to come from pre-tax withdrawals, and expect little-to-no other income (such as pension income, dividends, Social Security, etc.) can use the method below to quickly estimate their future tax rate

Use $$Future\ annual\ income = (current\ pretax\ balance) * (1+r)^t * WR$$

In this equation,
 * r = Real rate of return on pre-tax investments, % t = Number of years until withdrawals start (e.g., at retirement) WR = Withdrawal rate from pre-tax accounts, %/yr

Reasonable guesses for r, t, and WR can vary widely within (and even outside) the following ranges:
 * r - from 2% to 6% (depends on market behavior and asset allocation within the pre-tax accounts) t - from 0 to ? (very dependent on individual circumstances) WR - from 3% (e.g., those who think the “4% rule” is optimistic) to 8% (e.g., those who want to reduce pre-tax balances before starting Social Security and Required Minimum Distributions)

For example, with current pre-tax balance = $375K, r = 4%, t = 25 years, and WR = 5%, Future annual income = $50K/yr in today's dollars. The federal tax bracket for $50K/yr Adjusted Gross Income (AGI) using current tax law is 12%. What the marginal rate will be depends on all the taxpayer's circumstances.

For comparison, if one assumes
 * r = 2%, t = 20 years, and WR = 3%, Future annual income = $17K/yr r = 6%, t = 30 years, and WR = 7%, Future annual income = $151K/yr

In other words, changed assumptions can produce very different results, so take a best guess now and update annually.

From this expected future income, subtract the appropriate standard deduction (below), and look up the income in today's tax rate table for your expected filing status. Add any expected state tax rate, and if the income is in the IRMAA range, a representative IRMAA rate as well.

Compare your estimated future marginal tax rate to your marginal rate today, making any adjustments for maxing out accounts, Saver's credit, and/or not getting the full employer match as applicable. If your estimated future marginal rate is lower than today, traditional contributions should be preferred. If your estimated future marginal rate is higher than today, Roth contributions should be preferred.

This method assumes no further contributions are made to traditional accounts, and so may make a low estimate for future balances and tax rates. Readers who calculate they prefer traditional, but think partial or total Roth contributions may be preferred, should conduct a more detailed analysis described below. However, readers who calculate Roth is preferred can be confident that is the correct choice.

Detailed method
A more detailed analysis may give a better answer, but is also more complex to perform. Assumptions about contribution type in the current year, and similar future years, affect the predictions for future income and tax rates, so more than one iteration may be required. See below for a method to estimate each common type of future income.

Pre-tax withdrawals
If you plan for the current year to be about the same financially as every year between now and withdrawal, the Future Value function ("=FV" in Excel) is useful for estimating future income:

$$Income = FV(r, t, -c, -b) * WR$$

In this equation,
 * r = Expected real rate of return on pre-tax investments, % t = Number of years until withdrawals start (e.g., at retirement) c = Planned annual pre-tax contributions, including employer contributions/match b = Current aggregate pre-tax balance WR = Withdrawal rate from pre-tax accounts, %/yr

If your plan is more complex, involving contributions changing in future years (eg. income expected to rise, catch-up contributions after age 50, large Roth conversions before age 70-72, etc.) then a more complex estimate using a spreadsheet may be needed.

Note that this estimate requires an expected pattern of traditional contributions. Begin with a "guess", which can be taken from the list of typical cases, or a prior year's analysis. If, at the end, this "guess" looks to be the wrong choice, you may need to revise that estimate and repeat the analysis.

Taxable investments
Investors with significant taxable accounts should account for yield income (interest, dividends, capital gains distributions) from these investments. At a minimum, the expected yield from taxable investments is:

$$Income = FV(r - y \cdot tr_{div}, t, -c, -b) * y$$

In this equation,
 * r = Expected real rate of return on taxable investments, % y = Expected yield from investments, % $$tr_{div}$$ = Average tax rate on investment yield t = Number of years until withdrawals start (e.g., at retirement) c = Planned annual taxable contributions b = Current aggregate taxable balance

If you plan on taking taxable withdrawals, the additional capital gains should also be included.

For a portfolio of mostly passive stock-based mutual funds, a yield of 2% is a reasonable estimate. Bonds and bond-based funds tend to yield higher, so this number should be adjusted upward if your taxable portfolio has a significant bond allocation.

Note that qualified dividends and long-term capital gains are taxed at reduced rates, and these forms of income stack "on top" of other income that is taxed at ordinary rates. So, this income may have little effect on your marginal tax rate for pre-tax withdrawals. However, qualified dividends and long-term capital gains are taken into account for taxation of Social Security benefits, and can add marginal rate to pre-tax withdrawals if the latter shifts the former up into a higher bracket.

Social Security
If you plan to retire near the age when you expect Social Security payments will begin, include the expected payment, in the percentage that will be taxable according to the laws for taxation of Social Security benefits.

Note that taxation of Social Security benefits phases in at a rate of either 50% or 85% for each dollar of other income. Therefore, if your total income is in the phase-in range, you can expect a marginal tax rate 1.5x or 1.85x your tax bracket. Typical planning strategies are to come in either just below, or far above, this rate "spike." If your plan has your income around this spike, reconsider your choice of contribution type and rerun the analysis if necessary. An example of this planning is shown below.

Several online tools exist for estimating your future Social Security benefit, on the Social Security Administration (SSA) website and elsewhere.

Other income
Include any other expected forms of taxable income, such as a pension, income from part-time work, royalties, inherited traditional distributions, rental property income not expected to be sheltered by depreciation, etc.

Standard deduction
As of 2022, the standard deduction is $14,700 (single) or $28,700 (married filing jointly) for taxpayers age 65 and older, or $12,950 (single) or $25,900 (married filing jointly) for taxpayers under age 65. Subtract the most appropriate value from your expected future income.

It's uncommon (but not impossible) for retirees to itemize deductions, so assuming the standard deduction is usually safe. If you expect to itemize deductions, for example due to large charitable donations, an estimated itemized deduction may be used instead.

IRMAA
If you predict you'll be in the range of the 1st through 3rd of the IRMAA tiers, add a representative tax rate to your overall marginal tax rate, about 5% as of 2022. If you are confident you'll be in the 4th IRMAA tier or above, or well below the 1st IRMAA tier, do not add any tax rate for IRMAA.

The "spike" behavior of IRMAA makes planning difficult, as actual IRMAA marginal tax rates will be either large (if an IRMAA tier threshold is crossed) or zero. Applying an average tax rate give as much accuracy as is possible for a long-term analysis. For a shorter-term analysis, such as Roth conversions in early retirement, using exact tier thresholds may make sense, although there is still the problem of the two-year delay.

Analysis
Look up the total income minus deductions in today's tax rate table for your expected filing status, including any Social Security phase-in, and adding any expected state tax rate and IRMAA rate, as applicable.

Compare your estimated future marginal tax rate to your marginal rate today, making any adjustments for maxing out accounts, Saver's credit, and/or not getting the full employer match as applicable. If the numbers are close or equal, it likely won't make much difference which you pick, so you might choose to mix traditional and Roth contributions, to take advantage of tax diversification.

If this analysis shows that your planned contribution choices were correct, you can be confident in that result. If not (eg. assuming traditional contributions in the current year and similar future years says Roth is preferred), then rerun with different assumptions. If neither choice appears correct (eg. assuming traditional contributions says Roth is preferred, and assuming Roth contributions says traditional is preferred), the optimal choice is some split; see Straddling brackets.

Results
Most investors will find that traditional contributions are better during their normal working career, for two reasons:
 * Retirees usually need lower income than while working to maintain the same standard of living, because they are no longer saving for retirement, expenses for children have ended, the mortgage is probably paid off, many retirees relocate to lower cost-of-living areas, work-related expenses have ended, life and disability insurance are no longer needed, etc.
 * Retirees pay a lower tax rate on the income they do draw, because lower income usually means lower tax rates, many retirees live in low-tax or tax-free states, Roth withdrawals and return of basis from taxable investments are tax-free, capital gains are taxed at a reduced rate, payroll taxes have ended, Social Security is 15-100% federally tax-free and not taxed by many states, HSA withdrawals for medical expenses are tax-free, etc.

There are plenty of exceptions to this rule, however, including those with very high or very low incomes, planning to move from low-tax to high-tax states, heavy savers who expect more taxable income in retirement than while working, planning to leave money to higher-tax heirs, working around unusual tax laws, and others. A non-exhaustive list of cases where Roth contributions are preferred is above.

If you currently have very little tax-deferred retirement savings, your calculated retirement tax rate will be very low, so you’ll get a big value by contributing more. In fact, due to the federal standard deduction, the first $14,700 or $28,700 you withdraw in retirement each year (assuming you're over age 65 at the time) should be tax-free. (These values decrease slightly, but not much, with significant Social Security income). Assuming a 4% withdrawal rate, that corresponds to an account balance of $367,500 (= $14,700 / 4%) or $717,500 (= $28,700 / 4%) that can be accessed federally tax-free, and these figures should grow with inflation.

As your tax-deferred balance rises, so will your expected tax rate, but as long as it’s less than your marginal tax rate now it still makes sense to contribute to tax-deferred accounts. If your expected retirement marginal tax rate ever reaches or exceeds your current marginal tax rate, and you still want to save more, then additional savings should be done in a Roth account.

Example
A single investor earns $200,000 gross income and has a marginal tax rate of 32%. He plans to retire in 25 years at age 65. He currently has $450,000 in traditional (tax-deferred) savings, contributes $20,500 per year to this account, and expects it to grow at 8% after fees, and assumes 3% inflation. He also has a $50,000 taxable account, to which he contributes $10,000 per year, with an expected growth of 8%, a yield of 2%, and a dividend tax rate of 15%. He also expects to take $3,000 per month inflation-adjusted Social Security benefit immediately after retiring, of which he expects 85% to be taxable. He does not expect any additional income in retirement.

His 401(k) allows either traditional or Roth contributions; which should he be making?

Given his relatively high income compared to his savings, it's reasonable to guess that continuing to make 100% traditional contributions will be best. Assuming he continues to make $20,500 traditional contributions, his predicted retirement marginal tax rate could be calculated as follows:

Under the current tax bracket structure, his future marginal rate with that income is predicted to be only 24%, which is less than his current marginal rate is 32%. The assumptions in this analysis (maximum ongoing traditional contributions, and maximum Social Security taxation) represent a "worst case" for taxable income in retirement.

Because his marginal rate is still predicted to be less than today, the guess was correct, and he should prefer traditional contributions to Roth for the current year. He should repeat this analysis each year, accounting for actual investment growth and tax law changes.

State taxes
Consider state taxes as well as federal taxes in your tax rate comparisons, both for the state you live in and for the state you expect to retire in.

Some states do not allow deductions for traditional account contributions, or only allow them for some types of contributions (New Jersey, for example, allows deductions for 401(k) but not 403(b) or IRA contributions); if you live in such a state, the Roth has an advantage.

If your state allows a deduction but you might retire in a state which has no tax or will not tax your traditional IRA withdrawals, then the traditional IRA has a potential advantage.

Conversely, if your state has no income tax but you might retire in a state which taxes traditional IRA withdrawals, the Roth has a potential advantage.

Estate planning
For those planning on leaving a significant estate to their heirs, multi-generational effects should be considered.

For example, if you are a high earner in the 32% tax bracket, and expect to be throughout retirement, but your heirs are lower earners in the 12% tax bracket, you should prefer traditional contributions - your heirs will receive a larger inheritance after tax.

Likewise, if you are in a lower tax bracket than your heirs, you should prefer to contribute to Roth accounts. If you plan to bequeath assets to a tax-exempt charity, that bequest should be from a traditional account as opposed to a Roth, because neither you nor the charity will pay taxes on the funds, and the charity will receive a larger donation.

The federal estate tax exemption, $12.06M for individuals and $24.12M for married couples as of 2022, applies regardless of whether the accounts being bequeathed are traditional or Roth. Because Roth dollars are worth more than traditional dollars, investors who are at-risk of being above the estate tax exemption limit should prefer Roth investments, and/or perform Roth conversions. Even if there is a marginal tax rate disadvantage, your heirs could possibly receive more after taxes by avoiding or reducing double taxation. You will increase the after-tax value of your estate to your heirs when you make Roth contributions and do Roth conversions when:

$$MTR_h > MTR_n \cdot (1 - MTR_e)$$ (derived here)

where:

$$ \begin{align} MTR_h & = \text{predicted marginal income tax rate for your heir} \\ MTR_n & = \text{marginal income tax rate for you now} \\ MTR_e & = \text{predicted marginal estate tax rate on your eventual estate} \\ \end{align} $$

There are other ways to lower the value of one's estate (eg. gifting money during your lifetime) or otherwise avoid estate tax, so this method should be weighed against other options.

The SECURE Act of 2019 now requires inherited IRAs to be completely distributed by the end of the tenth calendar year following the year of the owner's death. If you expect to leave large IRAs as part of your estate, such that withdrawals will likely push your heirs into a tax bracket higher than yours is now, favor Roth contributions and conversions during your lifetime. See the Stretch IRA page for strategies for large inherited IRAs. For small IRAs that will not affect your heirs' tax status, simply comparing your marginal tax rate to your heirs' current rate will be sufficient.

Opportunity to convert later
If you contribute to a traditional IRA, you can convert to a Roth IRA in a later year. If you contribute to a traditional 401(k) and leave your employer, you can roll the 401(k) into a traditional IRA and then convert it later, or roll it directly to a Roth IRA. Your income (and therefore marginal tax rate) might be lower in a year when you separate from an employer. In either case, you may come out ahead if you can convert in a lower tax bracket, because you pay the taxes in the year of conversion instead of the year of contribution. There is no analogous "traditional conversion" whereby you can move money from a Roth account to traditional and reduce your taxable income, so this is an advantage for traditional accounts.

This increases the benefit from using traditional accounts when you retire in a low tax bracket. If you retire in a 12% tax bracket before taking Social Security, and don't need the whole 12% tax bracket for living expenses, you can convert part of your traditional IRA to a Roth at 12%, reducing the amount you will have in the IRA when you start taking Social Security.

But if you expect to retire in the same tax bracket, this is not a significant extra advantage for the traditional accounts. If you are usually in a 22% tax bracket and retire in a 22% tax bracket but happen to have some years in a 12% bracket (large deductions, unemployed part of the year, one spouse takes off from work or works part-time to care for children), you can convert up to the top of the 12% bracket in those years, and you can make those conversions from any traditional accounts you have, whether or not you have Roth accounts.

Required Minimum Distributions
Traditional accounts have the disadvantage of having Required Minimum Distributions (RMDs) begin at age 72. (Roth 401(k)'s have RMD's as well, but can easily be rolled over into a Roth IRA upon retirement, and Roth IRA's do not have RMD's). RMD's are a reasonable percentage of the account balance, but if you expect to want to leave large IRAs as part of your estate and RMD's would hinder this goal, then prefer Roth contributions.

Tax risk
If all else is equal (that is, you expect to retire in the same bracket, and never to have the opportunity to convert in a lower bracket), the Roth account has a slight advantage because there is less tax risk. You might not retire with the same marginal tax rate that you expect, either because tax rates change or because your taxable income is higher or lower.

Traditional accounts have a slight advantage when future income is uncertain. Choosing traditional today and being wrong usually means you have more money than you expected in retirement, which is not the worst problem to have. But choosing Roth today and being wrong means you had a significant shortfall in savings for some reason. The size of this asymmetry and whether it should impact decisions today is debated.

Another risk for MFJ filers is the death of one spouse, leaving the survivor with single filing status and its higher marginal rates. This risk would be partly mitigated if the spouse's death substantially reduced household expenses. If one or both spouses has health issues, it may make sense to bias toward Roth accounts to insure against this possibility.

Tax diversification
Tax Diversification is the principle that having assets spread across different kinds of accounts (traditional, Roth, taxable, etc). The further you are from retirement, the harder it is to predict what tax law will be.

By diversifying between current and future tax rates, you effectively provide yourself insurance against large tax rate changes (up or down). Also, it may be the case that there will be certain steep phase-outs, or "bumps" in marginal rates in the future (eg. the current Social Security taxation bumps). Having the flexibility to control your taxable income to some degree might allow you to better optimize around future tax laws.

Conversely, if you only have traditional investments, you will be required to withdraw RMD's or whatever you need to live on, and pay whatever tax results. Even if the traditional vs. Roth analysis described above favors one type or the other, there is a potential advantage to having a mix.

Investment options
You may have different investment options in traditional and Roth accounts. If your employer offers a traditional 401(k) but not a Roth 401(k), then you must use traditional accounts if you invest in the 401(k). If you are over the income limit for a deductible traditional IRA, then you must use a Roth account if you invest in an IRA (a non-deductible IRA cannot be better than either a deductible or Roth account). The choice of account, or benefits within the account, may be more important than the different tax treatment of traditional and Roth accounts.

Employer match
If your employer matches 401(k) contributions, this is by far the best investment you can make, as it has an immediate return equal to the match rate. Therefore, regardless of the quality of your employer's plan, you should get the maximum match before investing anywhere else.

If your employer offers both traditional and Roth accounts, any match goes to a traditional account, and the match is calculated without regard to whether your contribution is traditional or Roth. Therefore, if you cannot contribute enough to a Roth account to get the maximum match, you can get a larger match for the same out-of-pocket cost by choosing traditional contributions. You should choose traditional contributions when:

$$MTR_w < \frac{(1+m) \cdot MTR_n}{m \cdot MTR_n + 1}$$ (derived here)

where:

$$ \begin{align} MTR_n & = \text{marginal tax rate now} \\ MTR_w & = \text{marginal tax rate at withdrawal} \\ m & = \text{employer match rate} \\ \end{align} $$

Note that if $$m=0$$, then the equation simplifies to a simple comparison of current and future marginal rates.

Example
You can afford to contribute $3,000 out-of-pocket (after taxes) to an employer 401k, with both traditional and Roth options, that matches 100% of the first $4,000 of contributions. Your current marginal tax rate is 12%, and your expected marginal tax rate at withdrawal is 18.5% due to taxation of Social Security benefits. You can contribute $3,000 to the Roth account and receive a $3,000 traditional match, or $3,409 (=$3,000 / (1 - 12%)) to the traditional account, and receive a $3,409 traditional match. The break-even marginal tax rate at withdrawal is calculated as:

$$\frac{(1+100%) \cdot 12%}{100% \cdot 12% + 1} \approx 21.4%$$

Because the predicted marginal tax rate at withdrawal (18.5%) is less than this value, traditional contributions are preferred. If the match rate were only 50%, or if the marginal tax rate at withdrawal were 22%, then Roth would be preferred instead.

Investment quality and fees
Many 401(k) plans, and even more retirement plans of other types such as 403(b) plans, have inferior investment options.

If you invest in high-cost funds in a 401(k), you will usually lose more to the high costs than you can gain from any tax difference between the 401(k) and IRA.

Some plans have only high-cost options; in such a plan it is better to max out your IRA (traditional or Roth) before making unmatched contributions to the 401(k).

Other plans have some low-cost options, but have no options or high-cost options in some asset classes. In such a plan, you should prefer to invest enough in an IRA (traditional or Roth) to cover the asset classes with no good option in the 401(k).

Once your IRA is maxed out, it is usually worth contributing even to a bad 401(k). Conversely, some retirement plans, such as the Thrift Savings Plan, have better options than are available to retail investors in IRAs. If you have such a plan, you may prefer that plan to an IRA, even at a tax cost.

Investment quality and tax considerations can be combined into the same calculation, by using the Growth_factor in addition to the marginal tax rates. See also: Comparison between IRAs and employer accounts.

Example
You can either contribute $5,000 pre-tax earnings to a traditional 401(k) or a Roth IRA. Your marginal tax rate is 22% now, predicted to be 12% in retirement. The investment is expected to grow at 8% before fees in either case, but the traditional 401(k) charges a 1.00% expense ratio, and the Roth IRA charges a 0.04% expense ratio. Either investment would be withdrawn in 20 years. The future after-tax values of the two investments will be as follows:
 * Traditional 401(k): $5,000 * (1 + 8% - 1%)^20 * (1 - 12%) = $17,026.61
 * Roth IRA: $5,000 * (1 + 8% - 0.04%)^20 * (1 - 22%) = $18,043.56.

Assuming the investments are held for the full 20 year term, the fees in the 401(k) outweigh the tax savings, and the Roth IRA is a superior investment.

However, the tax savings from the traditional contribution is immediate, whereas the fees reduce performance gradually over time. In this circumstance, if you expected to separate from your employer well before the 20 year term, you could roll the 401(k) into either a low-expense traditional IRA, or the 401(k) at your new employer.

Depending on how long the money remained in the high-expense 401(k), you might come out ahead contributing to the 401(k) now.

Social Security benefits
One important exception is the phase-in of taxation of Social Security benefits. If you are in the phase-in range, you may experience a marginal rate in retirement of 22.2% or 40.7% despite being in the 12% or 22% brackets.

The 22.2% "bump" affects Social Security recipients with annual Social Security benefits less than $20,570 (Single) or $55,784 (Married Filing Jointly), and the 40.7% bump affects those receiving more than these values. See the main article for more details on where these formulas come from, and for useful visualizations of the phase-in effects.

As a function of annual Social Security benefit (SS), the 22.2% bump begins and ends at the following levels of income from other sources:

As a function of annual Social Security benefit (SS), the 40.7% bump begins and ends at the following levels of income from other sources:

The 40.7% bump is more abrupt, because it's bracketed by 22.2% below and 22% above. The 22.2% bump is bracketed by 18% below and 12% above. If you are reasonably close (10-15 years or less) to retirement and are in the benefits and income range where you may be affected by either bump, you should try to either come in under the bump, or go far above it, depending on which option is easier.

For those making traditional contributions, switching to Roth to lower taxable income in retirement might be the easiest option.

Example
A single investor, age 55, earns $80,000 gross income and has a marginal tax rate of 22%. He plans to retire in 10 years. He currently has $650,000 in traditional (tax-deferred) savings, expected to grow at 6% after fees, and has been making $12,000 annual contributions. He has no significant taxable investments. He expects to receive a $2,500 per month inflation-adjusted Social Security benefit starting upon retirement at age 65. He does not expect any additional income in retirement, from part-time work, investments income, rental properties, pensions, etc.

His 401(k) allows either traditional or Roth contributions; which should he be making? Making the overly-simplistic assumption that 50% of his Social Security benefit is taxable, his predicted retirement marginal tax rate could be calculated as follows:

By inspection of the tax bracket structure, his future marginal rate would be 22%, the same as today, so it would seem that traditional and Roth contributions would be equally valuable. His future income would be only slightly above the start of the 22% bracket ($40,525), so he might choose to favor traditional in case his predictions were off.

However, the picture changes when considering Social Security taxation. Because he receives more than $19,310 annual benefit, he is susceptible to the 40.7% bump. Using the above formulas, the bump begins and ends at the following levels of other income:

Unfortunately, his $40,444 traditional withdrawals put him right in the middle of the 40.7% bump. If he instead contributes $10,000 per year to his 401(k) as Roth for the next 10 years, his future income from traditional accounts will be reduced to $34,942 (=FV(6%-3%,10,0,-650000)*4%), keeping him below the 40.7% bump. He will still be in the 85% phase-in range for Social Security, but will be in the 12% bracket, so his marginal tax rate in retirement will be 22.2% (12% * (1 + 85%)).

Roth contributions are by far the better choice.

Straddling brackets
Note that the marginal tax rates now and in the future can be affected by the amount contributed to traditional accounts. For example, contributing the full $19,500 to a traditional 401(k) might bring an investor down from the 32% bracket into the 24% bracket. Likewise, contributing more to traditional accounts might raise the predicted future marginal tax rate such that it might cross into a higher bracket.

In these cases, the traditional vs. Roth analysis should be done for each dollar invested; contributions can be divided in any proportion. The higher the investment performance, longer the time horizon, and higher the contribution limit to traditional accounts, the more likely straddling becomes.

Example
A married couple earns $420,000 gross income and plans to retire in 30 years. They currently have $400,000 in traditional (tax-deferred) savings, expected to grow at 9% after fees. They can contribute up to $81,500 total to their 401(k) accounts, $40,500 of which can be traditional only, and the remaining $41,000 can be either traditional or Roth. They can afford to contribute $81,500 if all contributions are traditional, or the equivalent lesser amount if some are Roth.

They also have a $50,000 taxable account, to which they expect to contribute $5,000 per year, with an expected growth of 8%, a yield of 2%, and a dividend tax rate of 15%. They expect to each receive a $3,000 per month inflation-adjusted Social Security benefit, of which 85% will be taxable. They do not expect any additional income in retirement, from part-time work, investments income other than tax drag from the taxable account, rental properties, pensions, etc.

Should they make traditional or Roth 401(k) contributions with their $41,000 per year? For fully traditional contributions, their predicted retirement marginal tax rate could be calculated as follows:

Assuming the current tax system remains in effect, their future marginal rate is predicted to be 32%. Their current marginal tax rate with full traditional contributions would be 24% (taxable income = $420,000 - $81,500 - $25,900 = $312,600). On these assumptions, it appears as though they should prefer Roth contributions.

However, if the calculation is run assuming maximum Roth contributions, the result is different:

Their future marginal rate would therefore be only 24%, and their current marginal rate with full Roth contributions would be 32% (taxable income = $420,000 - $40,500 - $25,900 = $353,600), the opposite of before. The optimal solution is to split contributions between traditional and Roth contributions.

For simplicity, we can check six possible proportions, although in practice, spreadsheet or optimization software could automate this calculation to be more precise:

By splitting the contribution, this couple can lower their total taxes by staying within the 24% bracket both now and in retirement. Note that this analysis is extremely imprecise; it depends on future contributions being made, investments performing as expected, and the tax code remaining the same, most of which are very unlikely to occur.

However, current tax rates are well-known, so if the optimum traditional contribution is close to a step down in marginal rate, it's usually a good idea to contribute just up to that step, then contribute the rest to Roth. In this case, a traditional contribution of $54,000 is probably best, as it puts the couple's taxable income exactly at the 24%/32% bracket boundary at $340,100.

They would therefore also contribute $20,900 (=[$81,500 - $54,000] x [1 - 24%]) to Roth.

Maxing out your retirement accounts
The IRS sets a maximum contribution to retirement accounts. If you have reached this maximum, anything else you contribute must be in a taxable account that will (if you pay more than 0% on annual earnings or capital gains) lose money to taxes not incurred in either a traditional or Roth account.

The IRS contribution limits do not distinguish between traditional (pre-tax) and Roth (after-tax) accounts. Because after-tax money is worth more than pre-tax money, Roth accounts effectively allow you to contribute more than traditional accounts.

For example, if your marginal tax rate is 32%, a $20,500 Roth 401(k) contribution will tax-shelter $30,147.06 (=$20,500 / (1 - 32%)) of pre-tax earnings, whereas a traditional 401(k) contribution can only tax-shelter $20,500.

A fair comparison between Roth and traditional contributions when at a fixed-dollar limit must therefore also take into account the performance of the remaining money in a taxable account.

The after-tax amount invested in the taxable account is simply the tax savings from the traditional contribution, in this case $6,560 (=$20,500 * 32%).

The future after-tax values of the traditional account plus the taxable account can then be compared to the Roth account.

The equivalent conversion decision would be to convert a $20,500 traditional IRA to a Roth IRA, paying the $6,560 tax with money that would otherwise have been invested in a taxable account.

When contributing the maximum, traditional contributions have a higher after-tax value when:

$$MTR_w < MTR_n \cdot \frac{v - (v - 1) \cdot {MTR_{cg}}^*}{(1 + r)^t}$$

with

$$v = (1 + r - y \cdot MTR_{div})^t$$

and

$${MTR_{cg}}^* = MTR_{cg} \cdot \frac{r - y}{r - y \cdot MTR_{div}}$$

Variables are defined as:

$$ \begin{align} MTR_n &= \text{marginal tax rate now, for traditional contributions} \\ MTR_w &= \text{marginal tax rate for traditional accounts at withdrawal} \\ MTR_{div} &= \text{marginal tax rate on dividends} \\ MTR_{cg} &= \text{marginal tax rate on capital gains} \\ {MTR_{cg}}^* &= \text{effective marginal tax rate on capital gains assuming original basis} \\ v &= \text{growth factor on the taxable balance} \\ b &= \text{growth factor on the taxable basis} \\ r &= \text{total rate of return} \\ y &= \text{yield on the taxable balance} \\ t &= \text{time} \\ \end{align} $$

The formula is derived here. That page also contains a more complex formula that includes different rates of return for different accounts.

There are also two spreadsheets that have implemented the above equation:
 * The 'Misc. calcs' tab (near row 150) in the Personal finance toolbox.
 * Traditional versus Roth (401(k) or IRA)

Other factors affect this decision besides simply after-tax value. The combination of traditional and taxable money retains more flexibility than the Roth; traditional money can be converted to Roth in future years, and taxable money can be withdrawn at any time penalty-free. On the other hand, effectively sheltering more money inside retirement plans by choosing Roth can have asset protection benefits, and Roth accounts do not require RMDs.

Relationship to Roth conversions
In addition to contribution decisions, the above formula is also useful in the following Roth conversion decisions, as the math is analogous:
 * a) Doing a Roth conversion and paying the conversion tax from cash on hand (as opposed to paying the tax from the conversion amount).
 * b) Doing a Roth conversion to reduce Required Minimum Distributions (RMDs) when the RMDs will be reinvested in a taxable account instead of spent.

Situation b) is even more complicated because, unlike for a), a single equation for that situation has not been derived and a year-by-year spreadsheet approach is the best available. Two spreadsheets that have been published for this use are
 * McQ's spreadsheet
 * MDM's spreadsheet

Typical values
The following table calculates the break-even withdrawal tax rates for various sets of tax rates at different time horizons. All cases assume an investment with a total return of 8% and yield of 2%, of which 90% is taxed at long-term capital gains rates and 10% as ordinary income. If your withdrawal rate is predicted to be above the result in the table, Roth is preferred.

Note how dramatic the effect is for investors with high tax rates; even with a marginal tax rate today of 50.3%, after 40 years Roth contributions give more money after taxes with a withdrawal rate above just ~27%.

Very high income and wealth
Investors with high income and wealth, who expect to be in the top tax bracket now and in retirement, should usually prefer Roth contributions, for these reasons:


 * Being in the same (top) tax bracket now and in retirement eliminates any tax rate arbitrage between contribution and withdrawal, which is a typical advantage of traditional accounts
 * High tax rates on dividends and capital gains heavily degrade the performance of taxable investments, and shift the advantage more toward Roth accounts
 * The asset protection benefits of sheltering more money in Roth accounts are probably more significant for those with high income and wealth, and the higher liquidity of taxable accounts is probably less significant

Example
You are deciding between traditional and Roth contributions in your 401(k), with a contribution limit of $20,500. Your marginal rate now is 24%, your marginal rate in retirement is predicted to be 22%, your tax rate on qualified dividends and long-term capital gains are both 15%.

Your investments in any account are expected to have annual capital growth of 6% and a yield of 2%, for 8% total return, compounding annually. The yield is comprised of 90% qualified dividends and long-term capital gains distributions; the remaining 10% yield is taxed as ordinary income.

You plan to withdraw the money in 25 years. Are traditional or Roth contributions preferred?

The dividend tax rate on the taxable investment is:

$$MTR_{div} = 90% \cdot 15% + 10% \cdot 24% = 15.9%$$

The growth factors for the balance and basis of the taxable investment are:

$$v = (1 + 8% - 2% \cdot 15.9%)^{25} \approx 6.362$$

$${MTR_{cg}}^* = 15% \cdot \frac{8% - 2%}{8% - 2% \cdot 15.9%} \approx 11.72%$$

The withdrawal rate below which traditional contributions are preferred is:

$$24% \cdot \frac{6.362 - (6.362 - 1) \cdot 11.72%}{(1 + 8%)^{25}} \approx 20.09%$$

Despite the predicted withdrawal tax rate (22%) being less than the current tax rate, Roth contributions have a higher after-tax value. The spreadsheet linked above gives a similar value for a dividend tax rate of 15%. Refer to Figure 1.



You should decide whether the tax savings (about 2% of the contribution) is worth the partial loss of liquidity.

Saver's credit
Saver's Credit is effectively a match from the IRS on your retirement contributions if you have a relatively low income. The credit is given for contributions to either traditional or Roth accounts. However, there are two advantages which may make traditional contributions more attractive.

If you cannot afford to contribute $2,000 to a Roth account, then you can contribute more to a traditional account for the same out-of-pocket cost to get a larger match. In addition, the credit is based on your adjusted gross income. Contributions to a traditional IRA or 401(k) reduce your adjusted gross income and may make you eligible for the credit, or for a larger credit.

While qualifying for the Saver's credit, traditional or Roth can be decided upon using the following analysis. Traditional contributions are preferred when:

$$MTR_w < \frac{MTR_{n,T} - MTR_{n,R}}{1 - MTR_{n,R}}$$ (derived here)

where:

$$ \begin{align} MTR_{n, T} &= \text{marginal tax rate now, for the traditional contribution, including Saver's Credit} \\ MTR_{n, R} &= \text{marginal rate now of Saver's Credit for the Roth contribution} \\ MTR_w &= \text{marginal tax rate for traditional contributions at withdrawal} \\ \end{align} $$

Example
Consider a single filer with $30,000 gross income. For that person, up to a $2,000 contribution, $$MTR_{n,T} = 22%$$ and $$MTR_{n,R} = 10%$$.

For a $2,000 traditional contribution, the equivalent Roth contribution is $$R = $2,000 \cdot (1 - 22%) / (1 - 10%) = $1,733$$.

The withdrawal marginal tax rate for equivalent results is:

$$\frac{22% - 10%}{1 - 10%} \approx 13.33%$$.

If this investor expects the actual withdrawal marginal tax rate will be less than 13.3%, traditional is better. If more than 13.3%, Roth is better.

Real-world example
The methods described earlier in this article assume that one's marginal tax rate vs. contribution curve is either flat or decreasing, and one's marginal tax rate vs. withdrawal curve is flat or increasing. This behavior would be typical of a simple progressive tax system.

The US tax code, however, is not simple. Some credits, e.g., the Earned Income Tax Credit (EITC) and the Saver's credit, may apply only after a certain amount of low benefit contributions. Similarly, the Taxation of Social Security benefits may cause high rates on some portion of withdrawals, but past that portion the rates decrease.

Consider a couple with two children earning $54,000 per year gross income. Their marginal tax rate curve is shown in Figure 2.



The plot has negative values because the tax goes down as the 401(k) contribution goes up. The rest of this example follows the convention of ignoring the negative sign and refers to the rate at which tax was avoided when using "tax rate."

Their marginal tax rate goes through regions of 22%, 43%, 33%, 31%, and 21%, and there is a $200 spike due to a change in the saver's credit tier from 10% to 20%.
 * 22%: 12% bracket plus 10% saver's credit
 * 43%: 12% bracket plus 10% saver's credit plus 21% Earned Income Tax Credit phase-in
 * 33%: 12% bracket plus 21% Earned Income Tax Credit phase-in (saver's credit maximum contribution reached for this example)
 * 31%: 10% bracket plus 21% Earned Income Tax Credit phase-in
 * 21%: 0% bracket plus 21% Earned Income Tax Credit phase-in

Method
In order to capture the effect of the various peaks, valleys, and spikes, remember the operative definition of marginal tax rate: [total additional tax] / [total additional contribution]. In the chart above, the "Cumulative" curve shows that calculation for the given starting point.

For example, even though the marginal tax rate is 43% for contributions between $1,500 and $2,000, this couple would have to contribute $1,500 at only 22% in order to achieve that benefit. A $2,000 401(k) contribution would result in a tax decrease of $543.83, for a marginal tax rate of about 27% ($543.83 / $2,000). If the marginal tax rate on withdrawals is fixed, a simple method to optimize contributions is as follows:


 * 1) Starting at a traditional contribution of $0, calculate the marginal tax rates ([total additional tax saved] / [total additional contribution]) for all contributions between the starting point and the maximum contribution (limited by either IRS rules, or how much you can afford to save).
 * 2) Find the maximum marginal rate and the corresponding contribution
 * 3) If the maximum marginal rate is greater than your predicted marginal tax rate at withdrawals, make that traditional contribution.  Then return to Step #1 with the starting $0 reset to the traditional contributions so far. If the contribution marginal tax rate becomes lower than the expected withdrawal tax rate, contribute remaining retirement savings to Roth accounts.

It may be helpful to use charts such as the example given here to understand these situations. One can download the Personal finance toolbox Excel spreadsheet and use it for a wide variety of tax situations. Simply eyeballing the chart, it appears that somewhere between $13K and $14K would be the best traditional contribution. See below for more exact numbers.

Analysis
The married one-earner couple described above predict a 22% marginal tax rate in retirement. They can afford to save $10,000 after taxes to retirement accounts. How much should they contribute to traditional and Roth accounts?


 * Starting from $0 contribution, their maximum marginal savings rate is at a 401k contribution of $12,500, just enough to reach the 20% Saver's credit tier. This contribution results in a total tax savings of $4,169, for an incremental savings rate of ~33.35%. This rate is higher than the expected marginal tax rate on withdrawals of 22%, and the after-tax cost of $8,331 ($12,500 - $4,169) is less than the maximum, so contribute $12,500 to traditional accounts and try another iteration.
 * Starting from $12,500 contribution, their maximum incremental savings rate is at an incremental contribution of $1,100, resulting in an incremental tax savings of $342, for an incremental savings rate of ~31.1% ($342 / $1,100). This rate is still higher than the withdrawal tax rate, and the total after-tax cost is $9,089 ($1,100 - $342 + $8,331), so contribute an additional $1,100 to traditional accounts and try another iteration.
 * The marginal rate for all traditional contributions beyond $13,600, up to the $19,000 IRS limit, is ~21.06%. This is less than the marginal tax rate on withdrawals, so contribute no additional traditional money. Contribute the remaining $911 ($10,000 - $9,089) to Roth accounts. To maximize the saver's credit, the $911 should be contributed by the non-earning spouse. If both spouses are eligible for a 401k, having each contribute at least $2,000 will maximize the saver's credit, and then who contributes to the Roth doesn't matter.

These steps can be summarized in the following table:

The optimal retirement contributions for this couple are $13,600 to traditional accounts and $911 to Roth.

Additional examples may be found in Traditional versus Roth examples.

Direct calculation method
For situations where both the marginal savings rate and marginal tax rate at withdrawal are irregularly shaped (perhaps due to taxation of Social Security benefits), direct calculation of future after-tax value in retirement is best. One possible method could be as follows:


 * 1) For every possible traditional contribution, calculate the maximum amount of Roth and taxable contributions that can be made while still having enough spending money to cover expenses.
 * 2) For each case, calculate the future value (using "=FV" in Excel, or similar) of the traditional, Roth, and taxable accounts at retirement.
 * 3) Calculate the total taxes due in retirement, and the after-tax value of investment withdrawals. The set of contributions with the highest after-tax value is best.
 * 4) The analysis should be repeated every year.