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The Ultimate Quantitative Guide to Retirement: Roth IRA vs Traditional IRA vs Long-Term Gains

Jerry Zhang
Jerry Zhang
·

9 min read

This is unlike any retirement guide that you've seen before. Rather than generic advice that you'll commonly find in other blogs (Roth is the best so you should always max it out), I'm going to do a quantitative deep dive where I analyze each of the three types of retirement accounts assuming you use the same amount of money from the start. If you're scared of numbers and spreadsheets, this guide isn't for you.

Another disclaimer I must mention: this guide strictly compares between 3 types of retirement accounts (2 tax-advantaged and 1 normal). I know there are other ways to plan for retirement (such as real estate, which I also very much am a fan) but I won't consider those in this guide.

I won't be prescriptive in terms of telling you exactly what to do. I will, however, let the numbers do the talking and explain how different options are better during certain circumstances.

Now, I'm not a certified financial planner, so please don't treat my advice like it's coming from an expert. I'm simply a common person who's curious enough to crunch some numbers and share the results. To that degree, I made the ultimate spreadsheet that compares the Roth IRA, Traditional IRA, and Long-Term (saving with a non-tax-advantaged brokerage account).

If you're on this page, I assume you already know what a Roth IRA is and the difference between a Traditional IRA. If not, Google is your friend.

One more less-commonly known fact: everyone can contribute to a Roth IRA, even if you're above the income limit. Google Backdoor Roth IRA to learn more (or wait for my article on it).

I will do my best to keep this guide up-to-date. That said, if you notice any out-of-date information or have any other questions in general, feel free to comment below or get in touch.

Baseline Factors

Assumptions

Like any good quantitative observer, I list out my assumptions upfront:

  • The spreadsheet assumes all parameters are consistent annually. This includes contribution amount, market growth, income tax rate (yes, in life this may change as you earn more or less money per year, but I simplified here), retirement tax rate, and long-term tax.
  • The spreadsheet assumes that years working means years consecutively working. It does not account for any career breaks taken in-between.
  • The spreadsheet assumes that the end results in withdrawing everything in the retirement account. Practically, most people will probably withdraw just the amount they need monthly and let the remaining nest egg continue growing. Again, I took this simplification to show how much total would have accumulated at the time of the first withdrawal.
  • Regarding the neither, I assume that a regular brokerage account is used and the funds are not withdrawn until retirement so we can take advantage of lower tax rates of long-term capital gains.

Definitions

End – Amount of money in the nest egg by the time of the first withdrawal.

Income Tax – Amount of total upfront income tax paid throughout the years. This applies only to Roth IRA and Long-Term.

Withdrawal Tax – Amount taxed while withdrawing from the nest egg. This only applies to the Traditional IRA.Left – Money that we actually get to keep.

Left – Amount of money that actually belongs to us.

Growth Factor – How many factors our money grew compared to the amount we contributed.

Years Working – Years consecutively actively contributing to the nest egg.

Years Chilling – Years not contributing to the nest egg before first withdrawal. This is important because the nest egg continues to grow even without active contributions, thanks to compound interest.

2020 Tax Brackets

Just to provide a reference for how to fill in the income tax and retirement tax rates, here's a reproduced chart from the IRS.

Tax Rate Taxable Income (Single) Taxable Income (Married Filing Jointly)
10% Up to $9,875 Up to $19,750
12% $9,876 to $40,125 $19,751 to $80,250
22% $40,126 to $85,525 $80,251 to $171,050
24% $85,526 to $163,300 $171,051 to $326,600
32% $163,301 to $207,350 $326,601 to $414,700
35% $207,351 to $518,400 $414,701 to $622,050
37% Over $518,400 Over $622,050

2020 Long Term Capital Gains Tax

Unlike short-term capital gains–selling an asset for gain after holding it for less than a year–which is taxed like income, long-term capital gains–selling an asset for gain after holding it for longer than a year–makes it taxable at more favorable rates.

Tax Rate Taxable Capital Gains (Single) Taxable Capital Gains (Married Filing Jointly)
0% Up to $40,000 Up to $80,000
15% $40,000 to to $441,450 $80,000 to $496,600
20% Over $441,450 Over $496,600

The Spreadsheet

My spreadsheet has 4 sheets:

  • A high-level comparison between all 3 accounts
  • Detailed calculations for Roth IRA
  • Detailed calculations for Traditional IRA
  • Detailed calculations for Long-Term Gain
High-Level Comparison
Roth IRA Details
Traditional IRA Details
Long-Term Gain Details (regular brokerage account)

Here's the link to the spreadsheet. I've set this to view-only, so if you would like to play with it, you'll need to copy it into your own account. Then, you can begin modifying the parameters as you please, or you can even mess around with the rest of the spreadsheet.

I might even recommend that you follow along this guide with the spreadsheet to see what the numbers look like in each of the detailed sheets.

For the sake of brevity, I will only display the high-level comparison throughout the rest of this guide.

Clean Slate

Let's say we work for 30 years and then retire. Here's an absolute clean slate in a circumstance where there's no market growth and the income and retirement tax rates are the same:

Clean Slate

Not surprising. All three accounts have the same end result.

Now Let's Ride The Market

Of course, the market isn't going to stay still. If we take the S&P 500's average annual growth over the last several decades, we can assume a 7% growth rate.

Ride The Market

Now we start to see that the Roth IRA is pulling ahead. One thing to note is that the Traditional IRA is only a little bit ahead of the Long-Term Gains.

Chilling For A Bit

Who said we had to withdraw right away? (Well, for Traditional IRA, the government will eventually force you to withdraw to prevent you from evading taxes forever. You can read more about it by Googling RMD.)

Now, let's factor in some chill time. I consider this the number of years doing absolutely nothing. In other words, not actively contributing to the fund nor withdrawing.

Chilling Like A Villain

Now we can see the Roth IRA starting to really pull ahead due to the advantage of its tax-free growth. The upfront cost of paying taxes every year allows the funds to grow completely freely.

The Traditional IRA is also starting to pull ahead of the Long-Term Gains as well due to its tax-free growth, even with the withdrawal tax.

What If We Get A Raise?

We love it when we get raises. But how do our retirement accounts feel? Let's say we get such a huge raise that it bumps us up a tax bracket.

Raise Without Chill

If we compare the raise without chill with the ride the market numbers, our Roth IRA took a hit, but is still ahead. The Long-Term Gains took a hit too. The Traditional IRA didn't change.

Raise With Chill

If we compare the raise with chill with the chilling like a villain numbers, it's the same story: Roth IRA and Long-Term Gains took hits, while the Traditional IRA didn't change.

Does Roth Always Win?

From the examples above, it would appear so.

But if you work the numbers enough, you can arrive at a scenario where Traditional IRA beats Roth IRA.

Roth Loses

Though, this case is rare. You would need to:

  • Have a consistently lower market growth rate so the Roth IRA isn't able to fully take advantage of truly tax-free growth
  • Have very high income during the years you contribute
  • Retire extremely poor

Does Traditional Always Beat Long-Term Gains?

That's what it seems like so far. There are two patterns I've identified where Long-Term Gains can beat Traditional:

1. Retire Rich!

If your income is high during retirement, there's a chance Long-Term Gains can beat Traditional.

Retire Rich

That said, it still doesn't beat Roth.

2. No Other Source Of Long-Term Gains

If you don't have any other investments that provide long-term gains

In this case, your yearly compound gains for 30 years will not be taxed since your annual long-term capital gains will consistently be under $40,000.

No Long-Term Gains Tax

Notice how in this circumstance, Long-Term Gains becomes on par with Roth IRA.

But this is also quite rare–for your sake, I hope you have some other investments other than your retirement account. And if you do, your long-term tax rate won't be 0%.

Don't Underestimate Chill Time

Warren Buffet has called compound interest the 8th wonder of the world.

To that point, let me illustrate what happens if we prolong withdrawing from our retirement account as long as possible.

Normal (no chill)
Normal (chill 10 years)
Normal (chill 20 years)

If you pay attention to the growth factor, our investment for Roth IRA went from 3x (no chill) to 6x (chill 10 years) to 12x (chill 20 years).

Now, I know 20 years is a long time. But if you can delay withdrawing from your tax-advantaged accounts for as long as possible, you will be rewarded.

Something Bizarre

Say we go 50 years without withdrawing from our fund, but we vary the way we contribute.

50 Years – 30 Working 20 Chilling
50 Years – 20 Working 30 Chilling

Looking at the Roth IRA column, the growth factor rewards more chilling, even though the amount of money total is higher if we work more.

That's because when we contribute to the Roth IRA, we need to pay income taxes on our contributions. However, when we are just chilling, it's just growing completely tax-free.

Future Work

With this guide, I've only scratched the surface of the possibilities when it comes to retirement accounts. There are probably a good number of other obscurely weird scenarios that I haven't thought of yet.

Again, if you'd like to play with the spreadsheet itself, here's the link to the spreadsheet. If you find anything interesting that I haven't covered, please share it in the comments below.

Final Thoughts and Observations

And now, it's time for me to give my comments. Again, these are just my thoughts and not meant to be prescriptive in any way as your mileage may vary. Also, I'm not a certified financial planner so please consult an actual professional if you want professional advice.

I believe Roth IRA takes the crown for the vast majority of scenarios. You just simply can't beat the completely tax-free growth.

If the market rates do better than usual, your Roth IRA will capture those upsides without having to fork over any extra taxes, which is not the case for the Traditional IRA.

If you can delay withdrawing from your retirement account, the Roth IRA will continue to enjoy tax-free growth. Unfortunately, taxes will be paid when you withdraw from the Traditional IRA, which includes any growth accumulated during your chill time.

Of course, the Roth IRA isn't always superior–I have demonstrated that Traditional IRA is better if your income will be significantly lower during retirement. But we're talking about being dirt poor during retirement. Which, I'm pretty sure no one wants to be.

Also, this guide also applies to the comparison between Roth 401k, Traditional 401k, and Long-Term as well. If you're lucky enough where your employer offers you the option to do Roth 401k, I highly recommend you take it.

And in case you missed it or forgot, anyone (even if you're above the income limit) can contribute to a Roth IRA. Google Backdoor Roth IRA to learn more (or wait for my article on it).

I sincerely hope this guide was helpful to you. It took a good amount of effort to write and compile the spreadsheet. If you like this sort of in-depth content, please consider subscribing to my email newsletter for the latest and greatest.

Personal Finance

Jerry Zhang

Programmer, YouTuber, and amateur musician. I like to write too!