Roth IRA vs Traditional IRA

“Do the Math” Series

In the financial world you can find all kinds of advice. Some people will sell you a life insurance policy as an investment. That’s like using a parachute for a tablecloth: It may work to some degree, but that’s not what a parachute is designed to do. A parachute really has a better and higher use than saving your table from getting dirty. Your parachute tablecloth would be a huge hassle to use, and you would be right to question the sanity of someone selling you a parachute to cover your table.

Yes, there is a lot of bad advice on the market. There are companies with an entire sales force that is financially incented to sell you bad products. In an effort to counter the confusion and poor advice, I am writing a series of articles I call “Do The Math.” The goal is to take an impartial look using real scenarios and honest calculations to point you in the right direction. No sleight of hand or crafty ways to steal your money.

This is my nerdy side showing and I don’t mind saying so. I get excited by getting to the heart of a situation using math to promote understanding of a topic. I hope my fervor for proving what path is best will help you in your financial life. I have nothing to gain, and you have nothing to lose. With this article, I’m unpacking IRAs – Individual Retirement Accounts.

History and Types of IRAs

Let’s start with the origin of the IRA. In 1974 the Employee Retirement Income Security Act (ERISA) created Individual Retirement Accounts (IRAs) as a way to encourage employees without a pension plan to save for retirement. The original IRAs are beneficial because they allow employees to contribute money before paying taxes on it. IRAs were created with a cap on the amount of money a person can invest in them each year – currently $6,500 for most people – and a potential benefit of paying taxes when the funds are withdrawn. The thought is that funds will be withdrawn in retirement and the owner of the IRA might be taxed at a lower tax rate in retirement than during employment years. These pre-tax IRAs – we call them Traditional IRAs now – also come with a required minimum distribution (RMD). The RMD is a required amount of money that must be withdrawn after the IRA holder turns 72. If you die with money remaining in your Traditional IRA, those who inherit the money will pay taxes on it. That is the Traditional IRA in a nutshell.

Fast forward two and a half decades and the Taxpayer Relief Act of 1997 created a new form of IRA called the Roth IRA. The Roth allowed money that had already been taxed to be invested and withdrawn tax-free. Roth IRAs have income limits meaning on the surface, if you make too much money, you can’t invest in a Roth IRA. In 2022, “too much money” meant over $144K as a single filer or over $214K if married filing jointly. There is a legal loophole that people making more than those limits can use to invest in a Roth IRA, but that is a tip for another time. Roth IRAs also have a maximum contribution limit of $6,500 per year (which bumps up to $7,500 per year for people over 50). The Roth IRA is not subject to RMDs, so there is not a minimum amount of money that must be withdrawn based on age. Both Traditional IRAs and Roth IRAs have penalties if you take money out money before age 59 1/2. Is anyone else amused that the IRS makes laws based on your half-birthday? Finally, if you die with money in a Roth IRA, your heirs don’t pay any taxes because you paid taxes on the investment on the way into the account. That’s the Roth IRA.

Roth vs Traditional IRA

People in the financial world love a good debate, so they instantly sharpened their No 2 pencils and starting working to determine if a Traditional IRA is better or a Roth IRA is better. Some people swear by one, others advocate for the other, and still others will say use both or it depends. So what is the optimal way to invest in an IRA? This is where we…

I’ll work through three scenarios in case one size truly does not fit all, and I will build a model for each one. We can let the math tell us which option is best in each scenario. If we get a consistent pattern, we’ll declare one the clear winner. If results are mixed, we may have a draw on our hands, but I’ll do my best to point out the factors that swayed the results in one direction or the other. Below are three examples that I picked to look at variables like maximizing contributions, longer or shorter investment periods, and different income brackets to see what variables made a difference in the results. Here we go!

Scenario #1 – Max Out Your IRA

In this scenario, we have two investors. Ruth Roth makes the maximum contribution allowed by law each year into her Roth IRA account. Trevor Traditional makes the maximum contribution allowed by law each year into his Traditional IRA account. (Hint they are doing the same things, only the type of IRA is different.) Let’s see who retires happier.

Ruth and Trevor are both 46 years old now, so their maximum contribution is $6,500. (If they were 50 or older, they could contribute $7,500 per year.) As loyal investors, they have been making the maximum contribution since age 22. Back then the maximum contribution was only $2,000 but it has steadily been raised to the current $6,500 per year. All of that will be in our model. Assuming they have exactly the same investments that have performed at the S&P 500 average since 2000, they would have earned about 8.29% on their investments. To make the model simple, I give them that same average rate on their investment each year.

Ruth’s Roth

I’m going to try to stack the deck against Ruth in this example by making Ruth a high-wage earner. With a high income, her taxes are high. For our example, Ruth and Trevor will both make over $589,101 this year. You might think this is awesome – and it is! – but for our example the point is to make Ruth pay a lot in taxes before she makes her Roth IRA contribution. Because Roth only takes after-tax money, and because she makes such a great income, her money is taxed at 37% before she can contribute to her IRA. We are going to say she has been making enough money her entire career to be in the 37% tax bracket. That is highly unlikely, but let’s go with it because it increases her taxes paid. Again, we are trying to stack the deck against Ruth Roth. Only the IRS and I could be so diabolical. The maximum contribution has gone up over time for IRAs, but if we take this year as an example, Ruth has to make $10,317 of which $3,817 will be paid to the IRS so she can contribute the remaining $6,500 in after-tax dollars to her Roth IRA account. Yikes! She might start dumping tea into Boston Harbor in revolt.

Trevor’s Traditional

Trevor, on the other hand, has chosen the Traditional IRA to avoid paying all those nasty taxes before he makes his contribution. Crafty Trevor! He can contribute pre-tax dollars directly into his IRA (ha!) saving himself the $3,817 in taxes that Ruth had to pay (ha ha!). He believes this is a genius move and reminds Ruth about it every chance he gets.

Both Ruth and Trever have now invested $6,500 this year. Making identical maximum contributions each year from age 22 and getting exactly the rate of the market over that time, they now have identical balances of $337,996.97. Trevor has paid no taxes and Ruth has paid $70,476 in taxes on her contributions for the 25 years they have held their IRAs. Trevor is clearly in the lead here, but like the tortoise and the hare, the race is far from over.

Retirement Time!

Using our time machine, we fast forward to 2043 when Ruth and Trevor have a retirement party on the same day. They turn 65 and say adios to the working world. Assuming the IRA contribution limit remains fixed to keep the model simple, Ruth has now paid $152,405 in taxes on her contributions. Trevor has paid nothing. Trevor is clearly “winning,” but his tax bill is about to come due, but at a lower rate.

Ruth is able to withdraw her Roth IRA money tax-free – she already paid her bill in advance at a higher rate. I’m going to make a wild assumption here to try to stack the deck in favor of our friend Trevor. Trevor, buddy, you get to withdraw your money at a much lower 12% tax bracket. As single people, that means Trevor and Ruth are each making less than $44,725 each year. That is highly unlikely considering they were each pulling in over half a million dollars annually, but let’s pretend they paid a tax wizard to do some crazy good things to lower their official income to that level and keep them in the 12% tax bracket. It is an extreme version of why some people favor the Traditional IRA. The assumption is that being in a lower tax bracket will make the Traditional IRA a better deal. Let’s see if it worked.

Assuming that Ruth and Trevor live long enough to withdraw every penny from their respective IRAs, let’s look at the numbers. Both Ruth and Trevor contributed $259,000 over their working lives. As you recall, Ruth’s tax bill was $152,405 on that amount. Trevor will pay taxes on his contributions just like Ruth did, but he is taxed at the lower 12% rate. Taxes on his contributions equal a mere $31,140. Wow, he is still well ahead in our scenario and there is only one last figure to calculate. Ruth is done paying taxes. She paid her taxes on the money going in to her account, and with a Roth all money comes out tax free. Trevor is taxed 12% on his contributions and on his gains. Both of them have investment growth of $1,609,774. Nice! Trevor now has to pay 12% to Uncle Sam for each withdrawal. Assuming no more growth in the money, Trevor’s tax ball on his gains is (drum roll, please) $193,173. Here is our final score card:

	Ruth Roth	Trevor Traditional
Contributions	$259,500	$259,500
Growth	$1,609,774.15	$1,609,774.15
Total in IRA Account	$1,869,274.15	$1,869,274.15
Tax Rate	37%	12%
Taxes on Contributions	$152,405	$31,140
Taxes on Growth	$0	$193,173
Total Taxes	$152,405	$224,313
Total Money Withdrawn	$1,869,274.15	$1,644,961.25

When you look at this example, three things stand out clearly. First, even at a much higher tax rate during her earning years, by paying the taxes up front, Ruth saved almost $72,000 in lifetime taxes. Second, even with a lower tax rate, paying taxes on the growth of his money and the contributions means that Trevor paid significantly higher taxes. He was taxed on $1.8M instead of $259K. That made his tax bill larger. Third, because Trevor was paying taxes on the account as he withdrew money, he actually was able to only benefit from $1.64M instead of $1.87M. Not chump change for sure, but he got $224K less than Ruth did in retirement.

Scenario #1 goes to Roth. This example had textbook maximum contributions over a long period of time for high wage earners and a a very low retirement tax rate. Let’s look at a more realistic example of two people who started contributions later and then stopped well before retirement.

Scenario #2 – Delayed Contributors

Here we have Ralph Roth and Tracy Traditional as our two IRA owners. Early in their respective careers they each thought they didn’t make enough money to contribute to an IRA, so they didn’t. At age thirty, Ralph and Tracy each realized they were not saving for retirement and opened an IRA, Ralph a Roth and Tracy a Traditional. They each contributed the maximum allowed for the next twenty years. At age forty-nine, they stopped contributing so they could start to save up some money for their kids college. While they intended for this to be a temporary move, the truth is that life happened, and they never made another contribution to their IRAs again. This example spotlights a shorter period of contributions and significant investment growth.

Let’s see how it plays out after a few more details. Ralph and Tracy spend the first five years of their IRA contributing life in the 24% tax bracket and then they jump to 32% for the last 15 years. That just means that Ralph’s taxes are lower for 5 years and higher for 15. The last contribution is at age 49, and Ralph and Tracy both retire at age 66. For this example, I had their investments grow faster than that first example, but it is still within reasonable levels. I selected a growth rate of 11.94% per year. Some might think this is outrageous, but 11.94% is the average return on the S&P 500 since 1929. I intentionally included 1929 – the year of the great stock market crash and all the years of the Great Depression – but I excluded the three years from 1926-1928 leading up to crash where the market grew an average of over 30% per year. So yes, 11.94% is a fair number given my slightly conservative historical approach.

Here is the tale of the tape for Ralph and Tracy:

	Ralph Roth	Tracy Traditional
Contributions	$130,000	$130,000
Growth	$3,412,244	$3,412,244
Total in IRA Account	$3,542,244	$3,542,244
Tax Rate	24-32%	12%
Taxes on Contributions	$56,146	$15,600
Taxes on Growth	$0	$409,469
Total Taxes	$56,146	$425,069
Total Money Withdrawn	$3,542,244.08	$3,117,174.79

Well, it looks like Roth wins again. Ralph paid $368,924 less in taxes and as a result is able to withdraw $425,069 more than Tracy. The IRS should send a giant thank you to Tracy. Maybe they would if they weren’t so busy counting her tax dollars.

Scenario #2 – Roth wins. Roth is looking good. Let’s see if there is any way we can have Traditional come out on top.

Scenarios #3 – Worst Market Ever

In our final example, it’s not the end of the world, but you can see it from here. Okay, it’s not that bad, but this scenario is highly unlikely to happen, but I am only creating it to prove a point. Reggie opens a Roth, Toto a Traditional IRA and both contribute…blah blah blah…you know the drill. This time, I use the same numbers as in Scenario #2 with one significant twist. Their investments only grow by a tiny 4.5%.

Let me pause to put this growth rate into perspective for you. The gold standard benchmark for the stock market is the S&P 500, an index comprised of the 500 largest companies in the US. The index tracks the returns on those companies which tend to be stable companies that have grown over a long period of time. I pulled data from 1926 forward and never has the stock market had a loss over a 10 year period. It came close in 2008 with a paltry .67% gain over 10 years, but it was still in the black. The lowest return over any twenty year period since 1926 is 6.5% in 1948. That twenty year span included four consecutive down years in the Great Depression, a terrible 1937 with 35% losses, and some lean years with steady losses leading up to World War II. Exactly ten of those years (half of the time period!) had losses. Even with all of that headwind, the S&P returned 6.5% over that 20 year span. The average 20 year period returned 12.35%. The worst performing 37 year span is from 1972-2008 when the S&P 500 returned 11.2%. I tell you that to provide context around our next scenario where I have the S&P 500 returning 4.5% over 37 years. That is a ridiculously low number from a historical perspective. Laughably low. Seriously bad. It is about a third of what history tells you we can expect. You get the picture, but to prove a point, let’s go with it.

Here is the tale of the tape:

	Reggie Roth	Toto Traditional
Contributions	$130,000	$130,000
Growth	$320,340	$320,340
Total in IRA Account	$450,340	$450,340
Tax Rate	24-32%	12%
Taxes on Contributions	$56,146	$15,600
Taxes on Growth	$0	$38,441
Total Taxes	$56,146	$54,041
Total Money Withdrawn	$450,340.29	$396,299.45

Ah ha! We found it! If the market only performs at 4.5% (one-third of it’s average 37-year return) AND you are a high wage-earner AND you fall into a 12% retirement tax bracket (which would be a huge lifestyle drop from your working years) then a Traditional IRA comes out ahead on taxes by $2,105. The likelihood of all that happening is…well, sign me up for a lottery ticket if I can hit those odds because then I won’t need an IRA.

But we did it! We found a scenario where the Traditional beats the Roth. The key is really terrible returns because the taxes on the growth are minimal compared to the taxes on the contributions.

Let me put your mind at ease. If you invested in an S&P 500 index fund, this scenario will not be your future. Scenario #1 and #2 provide you with more typical returns and in those the Roth came out ahead by a few hundred thousand dollars. I suppose you could make a giant income and invest very, very poorly and pull off this negative unicorn event, but realistically with good investments that track the market (or anywhere close to it) and some normal tax rates during your earning years and afterward, the Roth will come out ahead.

Winner – The Roth IRA

So congratulations are in order for the Roth IRA. It wins. Go open a Roth IRA. But wait, not everyone qualifies to contribute to a Roth IRA. There is an income limit. If you make above a certain amount, the IRS won’t let you contribute directly to a Roth IRA. In 2024, if you file as a single filer to the IRS, you can make up to $146,000 and still contribute to a Roth IRA. If you have a modified adjusted gross income above $161,000, you cannot contribute. Between those two numbers, the amount you can contribute drops the more you earn. For married filing jointly, those limits are under $230,000 and over $240,000. To see more specifics, look at these tables on the Charles Schwab site.

That would really stink, if you earn too much and cannot take advantage of the Roth based on the numbers we just ran through. There is good news! If you earn too much to contribute to a Roth IRA, you can do what is called a backdoor Roth IRA where you contribute to a Traditional IRA and then immediately convert those contributions into a Roth IRA account. More on that in another article, but for now just know it is an option. It is 100% legal and allows everyone to benefit from the Roth IRA regardless of their income. For now, math has won the day again and shown us that the Roth IRA is superior to the Traditional IRA in almost all but the most edge case scenarios.

The Fine Print

^{To be fair to our old pal the Traditional IRA, there are some other factors to consider when you pick an IRA. In all our scenarios, the IRA holders contributed the most they could in years they made contributions. By maxing out their contributions, it compounded the growth of their investments faster. Maxing out a Roth means having the money for the contribution ($6,500 this year for most folks) AND having money to pay the taxes. In our scenarios, that means having $6,500 + enough money to cover your taxes. For you nerds (like me) who want to know that exact dollar amount you need before taxes, you can use this formula to calculate it:}

_{$6,500 / (1 – <your tax rate>)}

_{For example, if you are single filer making $70,000 per year, your tax rate is 22%, so your number would look like this:}

_{To max out the Roth at a 22% tax rate, you need to make $8,333.34 in order to pay taxes of $1,833.34 and still contribute $6,500. For the Traditional IRA, you only need to make $6,500 to contribute $6,500 because the contribution is pre-tax. If you are committed to maxing out your IRA, that difference means you have to earn more money to contribute fully to the Roth. You have seen the difference it makes on the back end when you retire, but it is fair to point our that you do need extra money up front to cover the taxes. If you don’t max out your IRA or if you use the taxes to subtract from your annual contribution, you will contribute less money to a Roth and that will make the Traditional a better deal because you are compounding less money over time in the Roth. If you plan to max out your IRA contribution each year, the Roth is the clear winner.}

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