Roth vs. Traditional IRA or 401k: The Math Behind This Important Decision

It’s without a doubt the most frequent question I receive from readers of this blog. People want to know whether they should put their retirement savings in a Roth or traditional retirement account.

I've written a lot about these retirement options. If you are new to retirement accounts, I'd suggest you start by reading some of the following articles:

The Ultimate Guide to Roth and Traditional 401(k) and IRA Retirement Accounts

Should You Max Out Your 401k Early in the Year?

How to Roll Over a 401k to an IRA

Roth and Traditional 401(k): Why not invest in both?

Calculating the Value of a 401k or IRA Retirement Account

Today we are going to look specifically at whether a Roth or traditional (pre-tax) retirement account is best.

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It’s All About Taxes (Mostly)

With some exceptions, the key issue when deciding on a Roth or traditional retirement account is taxes. Are the taxes you'll save today by making a pre-tax contribution to a traditional IRA or 401k higher or lower than the taxes you'll pay when you withdraw the money in retirement?

Particularly for those who are many years away from retirement, this question is almost impossible to answer with any degree of confidence. As you consider this question, keep in mind the following:

• Your current federal marginal tax bracket: Your marginal tax rate is typically the percentage you’ll save in taxes if you make contributions to a traditional retirement account (the contribution could move you into the next lowest tax bracket, splitting your tax savings from the contribution into two different percentages).
• Your state and local income taxes: We can't forget about the implications of this decision as it relates to state income tax.
• Taxes in the place you plan to retire: This may be an unknown for many. But if you do know where you'll be living when you begin taking withdrawals from your retirement account, this information can prove helpful in making the decision between a Roth and a traditional account.
• Your view of future tax rates: I have no clue what our taxes will look like decades from now, but many have very strong opinions on this topic. Personally, I don't make my decision on the type of retirement account on my view of future tax policies, but some do.
• Your tax rates before you retire: As you'll see in the section below on Roth conversions, there is a strategy to put away pre-tax dollars during your working years and then slowly convert the account to a Roth IRA later when your income places you in a lower tax bracket.

Roth vs Traditional--General Rule of Thumb

Let's first look at the general rule of thumb that I follow. Then we'll talk about the limitations of any general rule.

General Rule of Thumb

As a general rule, I look to my marginal tax rates for federal income tax as a starting point--

• Lower two federal tax brackets (10 and 15%) -> Roth
• Middle tax brackets (25, 28 and 33%) -> Roth and/or Traditional
• Highest two tax brackets (35 and 39.6%) -> Traditional with an eye toward Roth Conversion later

Now to the limitations. As noted above, a lot of factors go into the decision of a Roth or traditional retirement account. The focus above is on federal income tax. This is in part because state income taxes range from none to extremely high taxes. It's important to consider your local tax situation when making this decision.

Also, there is a wide range within the middle tax brackets, from 25% to 33%. On the lower end of this range, I lean toward a Roth account. On the higher end, I lean toward a traditional account. Regardless, keep in mind that it’s not all or nothing. You can choose to divide your contributions between a Roth and a traditional account.

Finally, the importance of the Roth conversion option cannot be overstated. We'll look at that below.

Traditional IRA or 401k vs. Taxable Accounts

Now it's time to look at the math. To start, let's first cover why a traditional retirement account is preferable to a taxable account.

Here we'll assume a $10,000 investment in a pre-tax 401k versus the after-tax equivalent of $7,500 in a taxable account. As you can tell from the numbers, we are assuming a marginal tax rate of 25%. We'll also assume that both accounts are invested the same way, and that over a period of time the investment grows 4x.

We’ll assume that the entire balance from both accounts is withdrawn at once in retirement and that no taxes are paid on the taxable account until the money is withdrawn. (No, these assumptions are not entirely realistic, but they are close enough for our purposes.) Finally, we’ll assume a capital gains tax rate of 20%.

401k Account

Initial investment: $10,000 Account grows to: $40,000 ($10,000 x 4) Taxes paid on withdrawal: $10,000 (25% of $40,000) After-tax balance: $30,000

Taxable Account

Initial investment: $7,500 ($10,000 less 25% in taxes paid) Account grows to: $30,000 ($7,500 x 4) Taxes paid on withdraw: $4,500 (($30,000 - $7,500 (initial investment)) x 20%) After-tax balance: $25,500

In short, tax-advantaged accounts can add a lot to a retirement nest egg. Now let's turn to the Roth vs. traditional retirement account analysis.

Roth vs. Traditional IRA or 401k (Don’t Max Roth Contributions)

In this example, we'll assume that we don't have enough to max out a Roth retirement account. This is an important assumption, as you'll see in a minute. We'll use the same numbers we used above.

Traditional 401k

Initial investment: $10,000 Account grows to: $40,000 Taxes paid on withdrawal: $10,000 After-tax balance: $30,000

Roth 401k

Initial investment: $7,500 Account grows to: $30,000 Taxes paid on withdrawal: $0 After-tax balance: $30,000

In this example given our assumptions, there is no difference between the two accounts. If I were faced with this situation, I'd select the Roth option. With a Roth, there is no Required Minimum Distribution. This means I can allow the money to sit in my account indefinitely after I reach retirement age, a significant advantage.

If, contrary to this example, we assumed that our tax rate was lower during our working years than in retirement, the Roth would be the better choice. If we assumed that our tax rate was higher during our working years than in retirement, the traditional retirement account would be the better option.

Roth vs. Traditional IRA or 401k (You DO Max Roth Contributions)

Now if we change the assumption so that we can maximize the Roth, the numbers change dramatically. The analysis also gets a bit more complicated. Here's why.

To compare apples to apples, we must calculate how much income we must earn to generate $22,500 (the current 401k contribution limit) in after-tax income for the Roth. Why? So that we can use the same figure for our traditional 401k comparison.

The 401k contribution limit is the same regardless of whether it is a traditional or Roth account. As a result, we will need to compare a Roth with a combination of traditional (up to the $22,500 contribution limit) and a taxable account (for the excess). Hopefully, the math will help make this clearer.

Assuming a marginal tax rate of 25%, how much do we need to earn pre-tax to generate $22,500 in after-tax dollars? The math is simple: $22,500 / (1 - .25) or $22,500 / .75 = $30,000. With this number in hand, let’s compare the two options starting with the Roth

Note: 401k contribution limits can change every year. Be sure to use the current contribution limits when comparing your options.

Roth 401k

Initial investment: $22,500 Account grows to: $90,000 ($17,500 x 4) Taxes paid on withdrawal: $0 After-tax balance: $90,000

The Roth analysis is simple. Now let's look at the traditional 401k equivalent

Traditional 401k

Initial investment (401k): $22,500 Account grows to: $90,000 Taxes paid on withdrawal: $22,500 After-tax balance: $67,500

Initial investment (taxable): $5,625 ($30,000 - $22,500 - 25% in taxes) Account grows to: $22,500 ($5,625 x 4) Taxes paid on withdraw: $3,375 (($22,500 - $5,625) x 20%) After-tax balance: $19,125

Total: $67,500 + $19,125 = $86,625

So why did the Roth come out on top just because we maximized our contributions? The reason is that with a Roth, 100% of our retirement nest egg belongs to us. With a traditional account, some portion belongs to Uncle Sam. True, we may not have to pay the taxes for decades. But eventually, we will have to pay the taxes. While that does give us some tax savings initially ($5,833 in our example), we must pay taxes on that amount and pay taxes on any gains we earn from investing that amount.

The result is what I call the Roth Advantage. If you max out your contributions and believe your taxes will remain unchanged now and in retirement, the Roth wins.

Roth Conversion

One available option is the conversion of a traditional IRA into a Roth IRA. You can also convert a traditional 401k to a Roth 401k in some plans. And even if you can’t, when you leave your job you can rollover the 401k to an IRA and then convert it to a Roth. This option has significant implications, particularly for this in the higher tax brackets during their working years.

For example, let's assume you are in the 39.6% marginal tax bracket during your working years. As a result, you are contributing to traditional retirement accounts given the significant tax savings.

Let's further assume that before you begin taking Social Security and Required Minimum Distributions from your pre-tax retirement accounts, you retire early. The result is that your taxable income would drop significantly, placing you in much lower tax brackets. It's during these early retirement years that strategic conversions to a Roth could save you a bundle in taxes. You'll have to pay taxes on the conversion, of course. But the rate will be significantly less than the 39.6% saved during your working years.

An important decision will be how much to convert each year. You don't want to convert so much in one year that it places you back into the higher tax brackets. Working with a tax professional can help you map out an ideal plan.

Backdoor Roth

Finally, I want to mention the Backdoor Roth strategy. For those whose income prevents them from either deducting a traditional IRA contribution or making contributions to a Roth IRA, the Backdoor strategy is ideal.

The strategy is simple to execute. You make after-tax contributions to a traditional IRA and then convert it to a Roth. While your contributions don’t enjoy any tax benefits, the investment grows tax-free. You can get more details on this strategy in my article on How to Use the Backdoor Roth IRA Strategy.