Trad vs Roth; (Marginal vs. Marginal) vs. (Marginal vs. Average); Wisdom from MDM

In the process of writing this blog, I’ve connected with several really smart people. One of the smartest I’ve encountered is reader MDM, best known for his Excel & tax wizardry (here). To my great disappointment, he doesn’t have a blog of his own, but instead contributes on the MMM forum among other places. A month or two back he generously emailed me out of the blue and helped me fix some bugs (mainly CTC) in my tax spreadsheet (link).

Last week, MDM emailed me questioning an assertion I made on the optimal “Trad vs Roth” decision that I made in my draft “book.” Since I learned a lot through the email correspondence that ensued, I asked MDM if I could make a post out of it and he obliged.

I’m simultaneously happy and sad when receiving an email from MDM. Happy because I’m about to learn something great. Sad because I’ve written something dumb on my blog to warrant an MDM email. Since my happiness from learning something great far exceeds the sadness from looking dumb, these are extremely well received emails.

With a healthy dose of humility, I admit I was wrong.

Below is a Cliff notes version of our email discussion. I have to warn you that it’s pretty dense and it’s possible only true tax-nerds would enjoy/understand/appreciate the subtleties of the conversation.

• Conventional wisdom says that you compare marginal while working vs marginal in retirement.
• In my draft “book”, I claim that the above conventional wisdom is bogus. In the book, I said the appropriate trade-off is marginal while working vs average in retirement. The reason why I proposed the above is because the average tax rate captures the combination of tax rates enjoyed in retirement (0% up to standard deduction, then 10%, then 12%, etc). For example, if the standard deduction is \$24.4k for MFJ and one’s Trad 401k/IRA income is \$24.5k, the taxes owed would be \$100*10%=\$10, corresponding to an average tax rate of 0.04% (=\$10/\$24,500). My claim was that this average tax rate in retirement better captures the true economics of one’s taxes in retirement than the marginal rate of 10% (where marginal, in this case, is defined as the tax rate on the last dollar of income earned).
• MDM contends that while the above is almost true, we can sharpen the above analysis since it fails to appropriately frame the decision at the margin today (whether to put another dollar in Roth vs Trad today). Let’s explain with an example. Below I’m plagiarizing from MDM’s email with simpler numbers for the purposes of illustration.
• Take a 30 year old couple with \$150k in a Trad 401k. Assume a 4% real return. If the couple contributes nothing more to the account, the Trad 401k will be worth \$486,510 (=\$150k*1.04^30) in 30 years when the couple is 60 years old. At that time, if they retire and withdraw 5% of their portfolio every year, that would produce \$24,325 (=5%*\$486,510) of income annually. Assuming no other source of income (no pension, no Social Security) and that the standard deduction remains at 2019’s \$24.4k level (not terribly unrealistic since we’re framing everything in real terms), the \$24,325 of future annual income would be taxed at 0% since it is less than the standard deduction.
• Thus, MDM asserts that in the above example the relevant tradeoff for the married couple while they were building up their first \$150k of Trad 401k balance would be their marginal tax rate while working vs their marginal tax rate on the withdrawal (where marginal is defined as taxes on withdrawal / size of withdrawal, not necessarily the definition of marginal as the tax rate on the last dollar earned). Since the entirety of the withdrawal is less than the standard deduction, the appropriate marginal rate in retirement is zero.
• However, if they were to add more to their Trad 401k/IRA balance today, the future value of the Trad 401k/IRA would as well (since FV = PV*(1+R)^N), as does the size of the withdrawal in the future. Future withdrawal amount = Withdrawal rate * PV*(1+R)^N.
• For the purposes of illustration, let’s add another \$50k to bring the couple’s Trad 401k/IRA balance to \$200k at the age of 30.
• Now, the future value is \$648,680 (=\$200k*1.04^30) and the annual withdrawal amount is \$32,434 (=5%*\$648,680). After subtracting the standard deduction, this leaves \$8,034 (=\$32,434-\$24,400) as the taxable amount in retirement. If the lowest tax rate in the future remains 10%, this would result in \$803 (=10%*\$8,034) of taxes. Consequently, the 30 year old should think of Trad 401k/IRA contributions in excess of ~\$150k as being taxed at the 10% rate….until the 10% bracket is filled in the future, at which point they’d think of subsequent contributions being taxed at the 12% rate…and so on.

The above reframing is so beautiful it makes me want to cry. It appropriately reframes the decision making process as comparing one’s marginal rate today vs one’s marginal rate in the future, where one’s marginal rate in the future is a step function that increases in today’s Trad 401k/IRA balance (and thus includes a 0% region, a 10% region, a 12% region, etc).

Again, MDM deserves the full credit for the above clarification. Prior to the discussion with MDM, I had yet to read/hear a discussion that so clearly articulates the optimal solution; one that appropriately frames the person’s decision of an additional \$1 Trad 401k/IRA contribution today, at the margin.

So how does this jive with GoCurryCracker’s strategy of never paying taxes again? GCC’s marginal rate (defined as taxes paid / size of Roth conversion) in retirement is 0% since he does Roth conversions up to the standard deduction. Therefore, he’s generating a ton of tax “alpha” by exploiting the differential taxation while working (>>0%) vs retirement (=0%).

So how can I use this reframing to assess how I’m doing? At the end of last month my tax deferred balance was \$472,363. If I started a 4% withdrawal rate tomorrow, that equates to \$18,895/year (=4%*\$472,363), which is less than the standard deduction of \$24.4k. Consequently, my entire Trad 401k balance would be taxed at 0% if I were to withdraw it (or convert it to Roth) slowly over time (a-la-GCC), starting tomorrow. Given my current federal + state marginal rate of 31%, I’d thus generate 31% of “tax alpha” by simply exploiting differential tax rates across my working and retirement years. In other words, it is only costing me \$0.69 to generate \$1 of after-tax wealth (assuming a future marginal tax rate of zero a-la-GCC). This is magical.

However, if I didn’t start withdrawals tomorrow, but instead let my Trad 401k balance grow another 10 years without contributing another penny, it would equal \$699,212 (=\$472,363*1.04^10) assuming a 4% real return. This translates to a \$27,968 (=4%*\$699,212 ) annual withdrawal amount at a 4% withdrawal rate, since \$27,968 exceeds the standard deduction of \$24.4k and begins to enter the 10% bracket. In this scenario (in which I don’t begin withdrawals tomorrow), I should thus think of any subsequent contributions to my Trad 401k/IRA as being taxed at a marginal rate of 10% (+ whatever my state tax rate is) in the future….until the 10% bracket is filled, and so on.

Given my current federal marginal rate of 24% and state marginal rate of 7%, I think I’m still well in the clear on over-saving in Trad accounts, particularly when considering the potential 7% tax savings by relocating to a tax-free state in retirement. For the foreseeable future (until my pre-tax balances get to several million), I don’t think I’ll get to the point where my future marginal rate exceeds 31%. After all, 4% of \$2M is only \$80k/year. With 2019 tax brackets, a MFJ household would have to earn over \$103,350 (=\$24,400 + \$78,950) to hit the top of the 12% bracket. I understand the U.S. has an impending fiscal crisis in the future, but my reading of the political climate predicts that the brunt of the burden will fall on high income types, not a retired couple withdrawing a relatively meager \$80k/year from a 401k, which is not too far off from the median household income in the U.S. In this sense, the 10Y period beginning on Jan 1, 2018 is an optimal period to build wealth under the temporarily low tax regime. Lucky me/us?

Below is the email chain with MDM. The underlined portions are the important parts (my emphasis).

Email 1: MDM kindly calling me out on my ignorance

Saw a recent comment in your blog (“Could you explain more why the right-most column is most important number in the tax code, and the one which should guide your “roth” vs “trad” decisions?”) and your response to “read the book.”

So I did.  Don’t recall if I had read it before, but in any case it’s a good read!

Well, except for the part about comparing marginal rate at contribution to an average rate at withdrawal. I’m hoping that part was written a while back and buried somewhere on your to-do list is an item to revise that…?

Yes, if one wants to look back over a career’s worth of contributions to evaluate whether the cumulative T vs. R decision was made correctly, and retirement income comes solely from traditional withdrawals, comparing the marginal contribution rate vs. the average withdrawal rate is correct.

But for someone wanting to decide what to do this year, the choice should be made by comparing the marginal contribution rate to the marginal rate to which this year’s contributions will be subject to at withdrawal.

Does that make sense, or are more details needed?

Anyway, I know the marginal vs. average thing seems so reasonable at first glance – because it did to me when I first heard it – but it isn’t how one should do a forward-looking evaluation. The https://www.bogleheads.org/wiki/Traditional_versus_Roth#Common_misconceptions section has a little more explanation.

Best regards,

MDM

Email 2: FP responding with a simple example, yet still not understanding MDM’s argument because I’m stubborn and I think I’m right

Thanks for the feedback on the “book”! I wrote it over the course of 2-3 days a couple years back as a potential “gift” to share with my students. It’s the exact information I wish someone had told me when I was in their shoes. It’s obviously not perfect, but I’d eventually like to finish it.

It’s evident you and I understand the tax code quite well. I think the residual source of disagreement is what we each define as “marginal”.

Assume
* MFJ
* 24.4k standard deduction
* 14.4k pension income taxed as ordinary income
* 10k roth conversion

What’s the tax on the \$10k roth conversion? Zero. We’re both in agreement here.

Now let’s increase the \$10k Roth conversion to \$10.1k.
Assume
* MFJ
* 24.4k standard deduction
* 14.4k pension income taxed as ordinary income
* 10.1k roth conversion

Taxable income = \$24.1k – \$24k standard deduction = \$100. Taxes owed on \$100 = 10% * \$100 = \$10.

The way I like to think about taxes, the first \$10k of Roth conversions are taxed at \$0 (since their marginal rate is 0% over that range of conversions) and the subsequent \$100 is taxed at 10% since that’s the marginal rate on any conversion in excess of \$10k.

What’s this household’s marginal rate in this second example?

For the purposes determining the taxation on the next dollar of Roth conversions, it’s 10%. That’s pretty obvious.

For the purposes of determining the tax rate on the entire 10,1k Roth conversion, it’s 0%*(10,000/10,100) + 10%*(100/10,100) = 0.0990%.

What I was trying to capture in the “book” is that latter of the two points above. It’s the average rate on the entire conversion that is balanced against the marginal rate while working. I’m fine if you call the above “average” rate as the “marginal” rate of the entire conversion. I simply prefer to think of “marginal” rate as the rate of the next dollar converted and define “average” as the rate on the whole Roth conversion.

Do you see my point here? I try to make the point in the “book” but it’s a subtle one that probably needs to be expounded upon.

Thanks again for the feedback!

– FP

Email 3: MDM patiently making his main argument through example

Hi FP,

That’s a good example. I see and agree (at least I think I’m agreeing with you) that the useful calculation is (change in tax)/(contribution or withdrawal amount being considered) with all other independent variables held constant. One could then dance around whether that ratio would be called average or effective or marginal or effective marginal or whatever. So far so good? I’ll assume so, and press on.

Let’s talk about the “amount being considered” in the context of contributions while working and withdrawals when retired. One could have a very similar discussion about when to do Roth conversions of money already in a traditional account but for now let’s do contributions while working and withdrawals when retired. We could get as granular as to consider every single dollar separately, and that in effect is what people do when saying “contribute to traditional while you are in the 22% bracket and switch to Roth after contributing enough that you are in the 12% bracket” and similar. But let’s keep it to one year’s contribution at a time.

Let’s also assume “other independent variables” such as pension, SS benefits, taxable dividends, etc., are not only constant but zero. No problem including them later but for now, simple as it gets: W-2 income from which 401k and IRA contributions can be made to either traditional or Roth while working, and withdrawals from those accounts when retired. Still good?

For calculation purposes, assume a single filer earning \$80K/yr contributing \$25K/yr (all at the start of the year…) starting at age 25 with zero net worth and looking to retire at age 55. Real investment returns 7%/yr, 2019 tax brackets, and a 4%/yr withdrawal rate will be used at age 55. We’ll call our filer Sam. At age 25 Sam sees \$0 in all accounts and decides to put all \$25K into traditional. A year passes and Sam turns 26.

Now that the table is set, we get into the meat of the discussion. Sam whips out a favorite Future Value calculator, determines that the \$25K contributed last year will grow to \$190K at age 55 and 4% of that is \$7.6K. Sam thinks “that’s less than the standard deduction so my expected marginal rate is 0%” and puts the second year’s \$25K into traditional. When Sam turns 27, the FV calculator says “add another \$178K to last year’s \$190K” to get \$368K. 4% of that is \$14.7K.

At that point Sam realizes the standard deduction at age 55 will be covered, and more, by withdrawals based on the first two year of traditional contributions. No more 0% bracket space available! But \$14.7K is still only the 10% bracket and Sam is saving 22% on traditional contributions so no reason to change.

Fast forward two years. Now the 10% bracket for withdrawals is also filled because Sam could stop making traditional contributions and still withdraw \$27.6K/yr at age 55, landing firmly within the 12% bracket. For the purpose of deciding on the fifth year’s contribution, Sam couldn’t care less that the average tax on that \$27.6K is only 6%. It’s the 12% marginal rate that would apply to any additional traditional contribution amount being considered that matters.

In fact, should Sam believe that the bracket rates would double twenty-some years from now, paying 24% at withdrawal for the privilege of saving 22% on the fifth year’s contribution is a terrible idea and Sam would logically switch to Roth contributions.

We could go on, but perhaps that’s enough for now. The main point is that the ability to make larger annual traditional withdrawals is built on the results of previous years’ traditional contributions. Analysis of the later years’ contributions must ignore the lower bracket rates because those are already “spoken for” by the earlier contributions.

Does that make sense?

Best regards,

MDM

Email 4: (A very dense) FP finally getting MDM’s point

Your response was brilliant. Thanks for giving me more food for thought!!!!

You’re indeed right that decisions should be made on the margin. And I really like how you took 4% of the existing future Trad IRA balance to fill up 0% brackets (and so on).

When I hear other bloggers/podcasters cover the topic, I never hear them discuss these intricacies in such detail.

So how do we generalize this?

• As one begins with a \$0 balance in a Trad IRA/401k, their future marginal rate is likely zero because 4% of future Trad balances is likely under the standard deduction in the future.
• As one’s Trad IRA?401k balance begins to grow, however, the above bullet point is no longer valid. What I claimed in my draft “book” is that we can simply compute the average rate and that will suffice for comparison to today’s marginal rate. Thanks to your brilliance, I now see how the above is sloppy since decisions are made on the margin.
• Consequently, the correct decision for someone to make is “marginal now vs marginal later” with the understanding that one’s marginal later is a function of existing Trad IRA/401k balances. This is really difficult to explain to someone! But it’s correct!

This has given me a lot to think about with respect to my own life. I’m wondering if I’m making any strategic blunders on my end. My marginal state rate is 7% and I think there is a good chance that I’ll relocate to a 0% state income tax state in retirement. Therefore, there is a 7% state tax alpha for any future Roth conversion. My marginal federal rate is 24%.

On the federal side, I think my main position of strength is my relative frugality (consumption somewhat near the standard deduction). Upon retiring, I can plausibly see how I can withdraw close to \$100k/year of income for free (per recent blog post). This is what Go Curry Cracker has done for a decade.

Who knows where tax rates will be in the future, but it it very likely they will go up. I’m of the opinion that they will go up much more for higher income types than those living near the standard deduction (like myself in the future).

What would MDM do given my financial situation? Trad or Roth? At work my 403b has a Roth option, so that would open the door for 19.5k/year more of Roth.

Thanks again for your time and expertise! It has been quite a productive exchange!!!

– FP

Email 5: MDM

Hi FP,

Your bulleted points all look good!

Your opinion on future tax rates is very similar to one in a recent Bogleheads post: “I might add that I spent the holidays with a person who was formerly a senior staffer on the House Ways and Means committee followed by decades as a K street lawyer-lobbyist specializing in federal taxation. She opined that for those in the lower and middle tax brackets, the odds of marginal brackets increasing in 2026 are very remote and in fact, considerable support for a modest simplification and decline from 12 and 22% to 10% and 20% and expansion of the EITC are being discussed. Any tax increases arising from the expiration of the current brackets will be all about the wealthy and in particular the extremely wealthy.

The above is of course subject to uncertainty but assuming a reversion to higher tax brackets across the board in 2026 as justification to pay more taxes at marginal or higher brackets now is an extremely poor base case assumption given political realities.

What would MDM do?  Good question!

Even looked at correctly w/ marginal vs. marginal, most people will still be better using traditional.  Your anticipated 7% state tax drop makes that even more likely. For “super savers”, however, Roth can become better, and maybe you are in that category.  If contributing the maximum to a Roth account, the “break even tax rate’ (withdrawal marginal rate at which traditional and Roth contributions have equivalent results) is somewhat lower than the contribution marginal rate. See rows 150-163 in the ‘Misc. calcs’ tab of the case study spreadsheet (CSS) to estimate “how much?” lower in your situation.

For a quick estimate of the traditional account balance needed to reach different federal marginal rates using a 4%/yr withdrawal ratio, see cells T2:V20 in the CSS.  You can add an “unavoidable” income amount in V4 for pensions, interest, etc.  These quick calculations don’t distinguish between ordinary and QD/LTCG rates.  If you weren’t planning to move after retirement, you might start thinking about Roth when your projected traditional balance gets up to \$2 million or so.  With the expected 7% in hand, you are probably good with traditional even at \$4 million or so.  At least, that’s off the top of my head with a quick look at the numbers.  I suggest you trust but verify. 🙂

Best regards,

MDM

9 thoughts on “Trad vs Roth; (Marginal vs. Marginal) vs. (Marginal vs. Average); Wisdom from MDM”

1. FP and MDM,

Thank you both for a very clear explanation. Its obvious that a lot of time was spent thinking through this.

One point I would add to complicate this is that you are using a greedy approximation of the optimal solution. That is, to get the optimal solution you need to look at all your earnings over your lifetime, not just the current year. That requires knowing the future, which is a fool’s errand if taken to the extreme. However, for some folks, I think it is possible to improve on the greedy solution.

An example:
Assume you have a PhD student, postdoc, medical resident etc.– Someone who expects to make a lot more in the future. They make \$50k/yr now but expect \$150k/yr in a few years. Also assume they have no Trad IRA/401k. Margin is 12% now versus 0% in the future. So we should choose a Trad IRA right? Well maybe.

Consider an alternate case. You work for 15 years and then FIRE. You have 2 million in future value in the Trad IRA/401k. You decide for fun to take a job being a park ranger. You have some taxable money you want to tuck away in an IRA. Let’s say the margin is 12% now versus 22% in the future. So you should put it in Roth right?

Both cases above are mathematically the same if you look at all working years at once. Fix the 2 million from your regular working years and decide how to deal with those low-earning years.

If you can *reasonably* predict that you will be working for many more years and making significantly more money during that time, it may make sense to put your current earnings in a Roth. It’s a guess about the future, but I’d argue more predictable in a lot of cases than the tax code.

Best,
Decius

Two caveats:
1) This requires predicting the future, so it is easier for someone like our fictional postdoc than someone climbing the corporate ladder. The latter person will likely make more over their career, but the increase will be less dramatic and predictable.

2) Although they are the same amount in the IRA “now”, the future value is dramatically less if your low paying years are later. So the calculation of the future margin will result in a slightly different result.

Reply
• Your argument is indeed valid. I was thinking of a similar example.

What if the hypothetical couple in the post inherits a Trad 401k (and thus start taking RMDs) around the time they retire? In this case, we’d see a corresponding increase in one’s future marginal tax rate, making Roth more appealing today. Consequently, the couple should plan accordingly when making the Roth vs Trad decision today.

Likewise, if a medical student is in their last year of residency and is about to have a massive and prolonged pay increase over the course of their lifetime, including an annual contribution of X% of their salary to mandatory Trad 401k participation (and employer match), I’m of the opinion that these future mandatory Trad 401k contributions should be incorporated into the resident’s assessment of their future marginal tax rate. Consequently, the 10% and 12% become really attractive to a resident for a Roth contribution since their future marginal rate is surely going to be high.

The above is not dissimilar to my current situation. My employer requires me to contribute a certain fraction of my income to a Trad 401a and they match a certain percentage. There is no getting out of it. Thus, for the purposes of my Roth vs Trad decision making today, I should appropriately account for those future mandatory contributions and their impact on my future marginal rate.

The above (that one’s future marginal rate is likely to increase through non-discretionary Trad 401k contributions or Trad IRA inheritances) is why I relay a simple rule of thumb to my students: Utilize Roth if your marginal rate is 10-12%. Utilize Trad otherwise. If my marginal rate was truly 10-12% (and I lived in a state with no income tax), I’d be stuffing every penny I could into a Roth account. This is precisely what I did as an engineer in Seattle (though tax rates were different then, of course). I don’t regret it one bit. For my students, the trivial 10-12% haircut now would provide relatively cheap insurance against future tax increases (resulting from tax law changes, inherited IRAs, etc). The only reservation I have with this strategy is that we live in a relatively high tax state (7%), so doing Roth now destroys the option value of relocating to another state.

I’m not sure I fully addressed your points, but I fully agree that knowledge about future income gains or inheritances will influence future marginal tax rates which will influence today’s Roth vs Trad decision. The better the knowledge is about these factors, the more informed of a decision one can make now.

It’s really a fascinating problem. Thanks again for the input!

Reply
2. If by “… look at all your earnings over your lifetime, not just the current year” you mean future earnings (not past) then we agree. Doctors in residency are a classic case of having a reasonable expectation for enormous income increases and thus making “Roth now” a reasonable bet for them.

One does have to be careful about implementing tactics that negate assumptions used to develop a given strategy. E.g., if one does an FV calculation for a traditional balance including a traditional contribution this year, but then decides the future marginal rate will be too high and thus makes a Roth contribution this year.

In short, I think all your points are valid. Now if we could just make those predictions accurately….

Reply
3. “Now if we could just make those predictions accurately …” indeed! Although I have closely followed tax policy with a strong professional interest for my entire life, I never could have predicted today’s brackets AND even more importantly, I never could have predicted that my effective marginal rate could be so different from my bracket rate.

Mostly retired now but below RMD age for six more years, and my bracket rate is 12% but if I do more than a small bit of Roth conversion, my federal effective marginal tax rate quickly gets very close to 50%! Tax torpedo effects in action as more ordinary income increases taxable SS widow’s benefits and both of those push my qualifed dividends from 0% territory to 15% territory.

(By contrast, I also did not realize that my state has so many tax breaks for retirees that my state effective marginal tax rate would be zero, even though NY is a famously “high tax” state! No need to move to escape state income taxes.)

Back when I started contributing to tax deferred 403b’s, tax brackets and effective marginal tax rates were much more likely to be aligned with one another. There were not so many provisions with phaseouts, let alone cliff effects, SS was not taxable no matter how high your income, what are now called “qualified” dividends were taxed the same as ordinary income, and IRMAA was not yet on the drawing board. And did not predict the SALT limitations. (On the other hand, I had no way to know that QCDs would be a thing!)

So many unpredictable changes and crystal balls are so cloudy that I think the only reasonable strategy is some degree of tax diversification. At least that is *my* strategy (currently at 23% traditional, 27% Roth, and 50% taxable.)

Reply
• Well said! It’s kind of depressing to get very scientific about the process when we don’t have a crystal ball. However, the important thing to me is to understand the economis of what is going on. And, thanks to MDM, I better understand the tradeoffs now.

For the retiree, it’s clear that diversifying between Trad/Roth is beneficial to you know. Especially given the added tax complexities (tax torpedo, etc). The Roth gives you a lot of freedom to avoid very high effective marginal tax rate cliffs.

What would you recommend for someone during their working phase now given the inherent imprecision with estimating one’s future marginal tax rate?

Do you think there is a reasonable effective federal marginal tax rate today above which Trad becomes the logical choice despite the Roth diversification benefits downstream? Given today’s tax brackets, I think <= 12% is a no brainer for Roth. In contrast, for most modest retirement balances, I think that Trad seems to make a lot of sense >= 22% today, particulary if there is a cross-state tax benefit in play (as I’m planning).

My federal + state is 24% + 7% = 31%. From your perspective, do you think I’m foolish for not locking in this tax rate in a Roth 403b for an extra 19.5k/year of Roth?

Thanks!
FP

Reply
4. Hi, I see that you recommend ROTH if one’s current tax rate is <=12%. Is this based on the assumption that the person's tax bracket will likely increase over time and hence better to save that 'allowance' for when your tax rate is higher.

But if say, someone does not expect their tax rate to go beyond 12% at any point in their career, wouldn't it still be better to save in a Traditional IRA to get the tax break and thus extra money for investment? Cos they are likely to pay 0% taxes after deductions in retirement too.

Reply
• I’m in agreement that Trad makes sense when your expected marginal rate in retirement is less than 12%.

Reply
5. You accidently wrote “With a healthy dose of humility, I admit I was wrong.”
You should have written: “With a healthy dose of humility, I am happy to learn something new”

Reply
• Good point!

Reply