So, I suspect I am missing something huge about this. But I notice there is a lot of talk about retirement accounts recently such as 401-Ks and IRAs. I understand these come in two flavors, traditional and Roth.


I understand Roth accounts entirely and the advantages, one deposits money, paying the taxes on it, it then grows tax free and later in life one has a larger amount of money than they deposited with and no tax liability, they don't pay any tax on the gains, this means they get capital gains income at a 0% rate. That is a very obvious advantage.


Traditional accounts however I fail to understand. It seems one deposits money without paying taxes, this money then grows to a larger sum over time from capital gains. Finally one takes this money out later in life, paying taxes on both the gains and the original deposits. It seems one ultimately pays taxes on all the money they saved, albeit later on.

Why is this advantageous to do as opposed to just paying taxes as one goes on the income and capital gains, particularly when taking taxable income in retirement can jeopardize social security payments and Medicare?


To give a concrete example, say between the ages 20 and 30 one places $5000 a year into either a normal brokerage account, a traditional retirement account or a Roth account, and keeps this money in the account for 30 years. (The numbers are contrived but are mostly to illustrate my confusion with only simple math.


Pays a total of $50,000 into account, pays taxes on $50,000. Makes... Say $400,000 in capital gains over 30 years. Withdraws $450,000 and has paid tax on $50,000.


Pays a total of $50,000 into account, pays no taxes on the $50,000. Makes... Say $400,000 in capital gains over 30 years. Withdraws $450,000 and pays taxes on all $450,000.


Pays a total of $50,000 into account, pays taxes on $50,000. Makes... Say $400,000 in capital gains over 30 years, pays taxes on the $400,000, but at an advantaged capital gains rate Withdraws $450,000 and has paid taxes on all $450,000, but less on the $400,000 of capital gains.

The core of my question, is why then does the traditional retirement account save money, it still seems one has paid taxes on the entire sum, and possibly losing the advantageous capital gains rate on it, that would otherwise reduce the taxes on a large proportion. What is the advantage?

Please note for this question I am explicitly avoiding the potential different rates of fees and returns for the various accounts, and assuming the same investment at the same expense ratio, as well as ignoring any potential employer match.

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    You can't just assume the same investment. The whole point of deferring taxes is that you can invest more initially. – Jean-Bernard Pellerin Jan 3 '19 at 22:57
  • @Jean-BernardPellerin, not when you're contributing the maximum. – quid Jan 3 '19 at 23:05

You are failing to consider the time value of money. Getting some nominal amount of money now has more value to you now than getting the same nominal amount of money later. If you invest an amount of money now and it grows into a bigger amount of money later, in a sense, you can think of this smaller amount now and the larger amount later to both have the same "value", even though their nominal amounts are different. (And conversely, you would much rather pay a certain nominal amount of taxes later than the same nominal amount now. So taxes paid later have less "value" paid than the same amount of taxes paid now.)

You wrote that you see the advantage of Roth IRAs, but not the advantage of deductible Traditional IRAs, so you might be surprised to hear that, on a mathematical level, if you start with the same amount of pre-tax money taken out of your income to contribute, and assume the same flat rate of tax at contribution and withdrawal, and make the same investment choices proportionally, and withdraw with no penalty, you are guaranteed to be left with the same amount of money at the end, no matter how much time has passed between contribution and withdrawal, and how much the investments have gone up or down in the meantime.

The problem with your example is that you are not comparing equivalent contributions. You are comparing the same nominal amount contributed, but the Traditional IRA contribution is a pre-tax amount, and the Roth IRA contribution is a post-tax amount, so they are not equivalent (one leaves less money in your bank account after taxes are done than the other). To compare equivalent contributions, you must start with the same pre-tax amount. So let's say, you want to contribute a pre-tax amount of $1000. Assuming a 25% tax, that is equivalent to a post-tax amount of $750. So you would compare a $1000 Traditional IRA contribution to a $750 Roth IRA contribution, as both would take away $750 from your bank account after taxes are settled.

Then, let's say it grows to 10 times the original amount over the years until you withdraw. For the Traditional IRA you have $10,000, and pay 25% tax to get $7,500. For the Roth IRA, it grows to $7,500 and you don't pay any taxes on withdrawal. The reason why those two are the same should be obvious -- both the result of being taxes, and the growth over the years, are multiplicative factors, and multiplication is commutative and associative, so it doesn't matter which order you multiply the factors in -- they are mathematically guaranteed to be equal.

This is despite the fact that you have paid a nominal amount of $250 in taxes in the Roth IRA case and $2500 in taxes in the Traditional IRA case. So it's not the nominal amount of taxes paid that matters. When those taxes are paid matters too. In a sense, you can say that the $250 of taxes at the time of contribution has the same "time value" as the $2500 of taxes at the time of contribution -- it's the amount the government would have if it invested the taxes the same way you did. We can also consider the time value of the money we invested -- since the money at the time of contribution can be thought of as having the same value as the money it grows into after an amount of time, paying tax once on the contribution amount at the time of contribution, is equivalent to paying tax once on the entire amount it grows into at the time of withdrawal -- in both cases, you pay tax once on the money.

Now, of course, in practice, there are many other factors that would make one or the other better. For example, the annual contribution limit for both is the same nominal amount, but the Roth IRA is a post-tax amount, so a Roth IRA has an effectively "higher" contribution limit than Traditional IRAs, i.e. for Roth IRA contributions close to the limit, there is no equivalent Traditional IRA contribution possible. Also, tax rates are rarely the same at contribution time and distribution time. And, tax rates are not flat, but progressive with brackets. Although contributions are limited to a few thousand per year and thus likely to be within the marginal bracket, withdrawals are likely to be bigger and dip into multiple brackets, so the effective tax rate of a withdrawal may be lower even if the marginal rate is the same. And Traditional IRA has other issues like taxable income could make Social Security taxable, and Traditional IRA has required minimum distributions, etc. But the point is, to a first approximation, Roth IRA and deductible Traditional IRA provide a comparable level of tax benefit.

Now if you compare this to a taxable account, you can see that the taxable account fares a lot worse. If you start with a pre-tax amount of $1000, therefore post-tax amount of $750, contributed into a taxable account, and it grows to 10 times, to $7,500, you would pay capital gains taxes on 9 * $750 = $6750. Even if it is a capital gains rate of 15%, that would be $1012.50 of taxes, leaving you with $6487.50. You would need a capital gains rate of 0% to match the advantage of Traditional or Roth IRAs. You can understand why this is worse if you consider that you already paid tax once on all the money you contributed when you contributed. Then, when the money grows into a larger amount later, this is money that grew from money that was already taxed; so, effectively, all this money has already been taxed once, time-value-wise. Then, when you withdraw, you tax a portion of the money (the "gains") a "second time". (It's taxed the first time from a nominal amount point of view, but we already know that point of view doesn't give you a useful picture.) And if you have an interest-bearing or dividend-bearing taxable account whose gains are taxed every year, that is even worse, because some portion of that money would be taxed, twice, three times, four times, etc. due to the "gains" (which grew from previously taxed money) being taxed every year.


The piece you're missing about a traditional IRA is the up-front tax savings that may apply. If you were taxed at 25% and able to deduct the full contribution then you could contribute 33% more to a traditional IRA (assuming room under the annual contribution limit) than you could to a Roth IRA for the same net cost, or have 25% more cash in hand after contributing. Note that 25% was just an easy number to use, there's a deduction phase out that varies based on whether you have a 401k.

If you don't qualify for deductible traditional IRA contributions, then the only benefit is deferred taxation on the growth, you'll pay tax in retirement at a likely lower rate than you pay now. If you can't get a deduction but can still contribute to a Roth IRA, then contributing to the Roth IRA is most likely the better option. If you can't get the deduction for traditional IRA contributions and can't contribute to a Roth IRA due to income, then the deferred tax is still most likely a benefit over a brokerage account. Though many would advocate a backdoor Roth contribution in that case.

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    "f you are taxed at 25% then you can contribute 33% more to a traditional IRA" Not really. You can get the same dollar amount in a Traditional IRA with less money out of pocket, but each dollar in a Traditional IRA is worth less than a dollar in a Roth IRA. – Acccumulation Jan 3 '19 at 23:07
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    @Acccumulation Traditional IRA dollars may or may not be worth less than Roth IRA dollars, the up-front tax deduction could beat future tax savings, there's no guarantee on growth or future tax rates. – Hart CO Jan 3 '19 at 23:18
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    No, a dollar going into a Traditional may be worth more than a dollar going into a Roth, but one dollar already in a Roth IRA is worth more than a dollar in a Traditional, because the tax on the Roth has already been paid. Each dollar in a Traditional represents one pre-tax dollar, but each dollar in a Roth represents slightly more than one pre-tax dollar. – Acccumulation Jan 3 '19 at 23:23
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    @Harper That assumes tax rate on both ends is the same and it ignores the deductible portion altogether. – Hart CO Jan 4 '19 at 5:27
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    @HartCO 30% and 40% isn't high in states that also tax. The $10k is pre-tax dollars so I'm not showing deductions, I'm showing taxes paid in cases that are not deductible. That is inverted from how most people think. Couldn't say all that in the space allotted. – Harper - Reinstate Monica Jan 4 '19 at 16:59

The point you are missing in the examples is what you are doing with the money saved on taxes with the Traditional IRA.

Assuming that that money is also invested, if you have a completely flat tax with no deductions on both contributions and distributions, a Roth IRA and a Traditional IRA are equivalent; because taxes are multiplicative, rate of return is multiplicative, and multiplication is commutative, it doesn't matter whether you pay taxes now or later.

As an example, assume you have $10,000 of pretax money and a flat tax rate with no deductions of 20%. If you left it for 10 years at a rate of return of 7% per year, you'll find that both 10000 * (1 - 0.2) * 1.07^10 and 10000 * 1.07^10 * (1 - 0.2) give you the same answer: $15,744.

Let's go to your examples:


Pays a total of $50,000 into account, pays taxes on $50,000. Makes... Say $400,000 in capital gains over 30 years. Withdraws $450,000 and has paid tax on $50,000.

Let's assume the same 20% flat tax rate with no deductions, so $10,000 is being paid in taxes. That means that $40,000 is being invested. Assume a x10 rate of return to get $400,000 in gains. End result: $440,000.


Pays a total of $50,000 into account, pays no taxes on the $50,000. Makes... Say $400,000 in capital gains over 30 years. Withdraws $450,000 and pays taxes on all $450,000.

No taxes are paid on the $50,000, so the extra $10,000 that would be paid can be invested. Because more is invested, more will be earned; instead of getting $400,000 of capital gains, with the x10 rate of return you'd get $500,000, for a grand total of $550,000. At a 20% tax rate, that's $110,000 in taxes, leaving you with $440,000, the same as the Roth.

The core of my question, is why then does the traditional retirement account save money, it still seems one has paid taxes on the entire sum, and possibly losing the advantageous capital gains rate on it, that would otherwise reduce the taxes on a large proportion. What is the advantage?

If your effective tax rate in retirement is lower than your effective tax rate while working, you will obviously wind up in a better position: you may pay more absolute dollars in tax, but that's because you have more money; the effective tax rate is lower.

However, because the US tax structure is not flat, and has deductions, even if the tax brackets and your income stay exactly the same in retirement as when working, you will pay less in taxes. This is because money that you contribute to a Roth account is generally taxed at your marginal (highest) tax rate, whereas money contributed to a Traditional IRA generally deducts from the marginal tax rate. Additionally, when you withdraw from your Traditional IRA, at least some portion of the withdrawal will fall under deductions and lower-than-marginal tax brackets, resulting in less overall tax.


I agree with you about Roth accounts. Pay the tax now and you only pay tax on your contribution not any gains. But the advantage of Traditional arrangements is as you put it "albeit later on."

Generally speaking people begin earning at the lowest tax rates. Through their lives they increase in earning power and thanks to progressive tax schemes your rate increases as you earn. The theory is, you avoid paying the tax now at today's rates because when you retire you'll be earning less and subject to a lower rate.

When you retire, you're not distributing $450,000 and paying tax at once. You're taking, maybe $30,000 for the year as income, which is subject to income related deductions. A single retired person who took $30,000 in distributions from their traditional account in 2018 will pay tax on $18,000 of income thanks to the $12,000 standard deduction. So you're only paying a tax on 60% of the distribution, at presumably a much lower bracket than you were in when you contributed the money. Granted, using your numbers, this is still a disadvantage because only 11% of your funds are contributed money ($50k/$450k). So 11% of the money is subjected to a 35% tax versus 60% of your money being subjected to a 10% tax.

Obviously, the assumptions related to future income taxation could be completely wrong. It's possible that we live in a higher rate and lower deduction future that totally invalidates the value of traditional retirement accounts. Additionally, Traditional arrangements are subjected to "Required Minimum Distributions" that Roth arrangements are not. People are generally working, living and earning longer and it's possible that RMDs would require you to take a taxable distribution before you would otherwise want to when you are still earning at your peak earnings and the distributed funds would be subjected to the then current top marginal rate.

But its also possible that we go crazy in the future and subject Roth distributions to income taxes as well.

The reality is most people want a deduction this year over any other consideration, and traditional arrangements offer that.

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    +1 for "most people want a deduction this year over any other consideration" Anecdotally, a couple of years ago I underpaid my federal taxes and if I did it the following year to the same extent, I would be subject to penalties. So I had 2 choices, increase my withholding (send more money to uncle Sam) or increase my traditional 401k contribution (keep the money for my retirement) - the choice was pretty obvious. – Glen Yates Jan 4 '19 at 19:10

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