I'm not a financial adviser--just an engineer who makes spreadsheets for just about everything. I finally got around to this one.

"If the tax is the same in the future, a 401(k) is the same as a Roth IRA," right? I read that here over 10 years ago. Someone posted an equation "proving" it. It has bothered me ever since. I thought it was a simplification. I knew it was flawed.

Well, it's practically the same, but not quite. I'll leave this here for you all to dismantle.

This message has been edited. Last edited by: Keystoner,

You would be better off comparing a traditional IRA vs. a Roth IRA.

You can have both 'types' within a company's 401(k).

I think the approach is that your taxable income will be lower when you retire so you will likely be in a lower tax bracket. Do the same calculation with a progressive tax and 4% withdrawal rate on the nest egg.

--K

quote:

Originally posted by Kranky:
I think the approach is that your taxable income will be lower when you retire so you will likely be in a lower tax bracket.

But this assumes/gambles that the tax rates will be the same in 20/30/40 years when retirement rolls around.

Which very well may not be the case.

Your spreadsheet is wrong for several reasons.

1) You didn't remove the taxes from the ROTH today. You will start with $5000 in the 401k but less in the ROTH.

2) Gains over time can be simplified to a single numerical factor. Add whatever the gains and losses are each year for that number. If your gains across the next 5 years are 5%, 6%, 3%, 6%, and 5%, you can calculate 1.05 x 1.06 x 1.03 x 1.06 x 1.05 = 1.276

Whatever you started with, multiply it by 1.276.

Your 401k would have $5000 * 1.276 in it.

Your ROTH would have ($5000 - $5000*TR) * 1.276 where TR is the tax rate today in %. That simplifies to $5000*(1-TR) * 1.276. All of that money will be yours tax free.

But your 401k gets taxed upon withdrawal. $5000*1.276*(1-TRB), where TRB is the % tax rate in the future.

Multiplication being commutative, those equations are the same. So only the tax rate today vs the future tax rate matter.

But it's worse than that!

3) Your future tax rate probably will not be lower. The government isn't likely to reduce income taxes in the future. The national debt and future obligations suggest future rates and brackets will not get friendlier. Your lifestyle probably won't decrease in retirement, so you'll withdraw from retirement accounts a similar amount as your final paycheck.

4) There are numerous tax traps in retirement. The higher your taxable income, the more penalties get applied. Your Social Security gets incrementally more taxed the higher your other taxable income. You pay more for health insurance, either on the marketplace before age 65 or for Medicare after 65. You are subject to RMD withdrawals from your IRA/401k at age 73 even if you don't need the cash to spend, pushing you into higher brackets.

5) States generally tax 401k and IRA withdrawals, but not every state. If you live in a high tax state while working, and move to a state in retirement that doesn't tax those withdrawals, the ROTH is slightly less advantageous.

6) Roth conversions are a bit complicated to optimize exactly when and how much to convert.

7) All retirement projections are guesses with many moving parts. In your lower income years, the ROTH is very attractive. In high income years the 401k may be more attractive, at least on the surface.

8) Paying taxes in retirement is very painful! Math aside, I'd rather have tax-free money in retirement by paying taxes when I worked.

There is no mandatory withdrawal requirements on Roth.

quote:

Originally posted by Fly-Sig:
Your spreadsheet is wrong for several reasons.

1) You didn't remove the taxes from the ROTH today. You will start with $5000 in the 401k but less in the ROTH.

2) <snip>

Your ROTH would have ($5000 - $5000*TR) * 1.276 where TR is the tax rate today in %.

No. I'm putting $5,000 in the Roth, not less.

And the rest of what you wrote is fine to discuss but it doesn't address the claim I'm investigating.

quote:

Originally posted by Keystoner:

quote:

Originally posted by Fly-Sig:
Your spreadsheet is wrong for several reasons.

1) You didn't remove the taxes from the ROTH today. You will start with $5000 in the 401k but less in the ROTH.

2) <snip>

Your ROTH would have ($5000 - $5000*TR) * 1.276 where TR is the tax rate today in %.

No. I'm putting $5,000 in the Roth, not less.

And the rest of what you wrote is fine to discuss but it doesn't address the claim I'm investigating.

But you have to pay tax on the ROTH up front. In your example you earned $100k and put $5k in the ROTH. So you paid, per your scenario, 25% of the $5k in taxes, which is $1250.

Thus your investment in the ROTH is actually $6125.

Whereas the 401k contribution is tax free, so your initial investment is indeed $5k.

As an example, $5000 invested over some time period at a rate which doubles it, yields a final value of $10,000.

For the 401k the equation is simple for what it is worth after a 25% tax. $10,000 * 0.75 = $7500. Which is C * R * (1 - T) where C is contribution of $5k, R is return over time, and T is % tax.

For the ROTH the equation is more complicated since you have grossed it up by paying taxes from elsewhere to keep the contribution at $5k. Invested the same as the 401k, your initial $5k is worth $10k. You pay zero taxes, so it is worth the full $10k.

You're $2500 ahead nominally with the 401k. But you paid $1250 in taxes years ago so as to have that initial $5k. So in raw dollars you're up $1250. But, you didn't get to invest that $1250 you paid in taxes years ago, so it didn't get to double over time. Thus you lost out on that doubling, which is $1250. So now you're even with the 401k.

I don't have time at the moment to put all that in a formula, but if you look at my previous post you'll see the formulas that apply if you start with the same amount and either 1) put it all in a 401k or 2) pay taxes and put the remainder in a ROTH.

The rest of that post shows that for very many people, especially those who are diligent savers and are thinking about all of this, the ROTH brings significant additional tax benefits beyond the simple tax rate now vs later question.

I'm putting $5,000 into the Roth account. This isn't complicated.

The correct answer albeit the harder one for most people is fund all of them. Fund them all ROTH if available. Realize that your 401k ROTH, only your contribution is ROTH, if your company matches their contribution is funded traditional 401k. Still a win.

If your company matches, fund your 401k first, ROTH if available then fund your ROTH IRA or traditional IRA and then backdoor convert it to ROTH.

quote:

4) There are numerous tax traps in retirement. The higher your taxable income, the more penalties get applied. Your Social Security gets incrementally more taxed the higher your other taxable income. You pay more for health insurance, either on the marketplace before age 65 or for Medicare after 65. You are subject to RMD withdrawals from your IRA/401k at age 73 even if you don't need the cash to spend, pushing you into higher brackets.

Don't forget net investment income tax (NIIT), if it applies in your case.

Yeah, max out your Roth IMO. I love the 0 tax on withdrawal from my Roth. I convert as much as I can each year from my Rollover IRA into my Roth...with concern for tax implications of doing it.

Think about RMD's in your future. I'll be facing them in 7 years and am trying to eliminate as much as I can from the rollover.

quote:

Originally posted by 6guns:
I convert as much as I can each year from my Rollover IRA into my Roth...with concern for tax implications of doing it.

I know you're retired. From where do you draw your spending money to pay for the tax on your conversions and for living? Is it from a brokerage account? I'm a few years away but this was my plan. I've already paid tax on that money and the tax on capital gains is less than ordinary income tax and it will keep me from tapping into the tax-deferred accounts prematurely.

quote:

Originally posted by Keystoner:
I'm putting $5,000 into the Roth account. This isn't complicated.

quote:

Originally posted by Keystoner:

quote:

Originally posted by 6guns:
I convert as much as I can each year from my Rollover IRA into my Roth...with concern for tax implications of doing it.

I know you're retired. From where do you draw your spending money to pay for the tax on your conversions and for living? Is it from a brokerage account? I'm a few years away but this was my plan. I've already paid tax on that money and the tax on capital gains is less than ordinary income tax and it will keep me from tapping into the tax-deferred accounts prematurely.

My income is from three sources:

Social Security.

Dividends from a taxable brokerage account and my Roth.

Rental income.

My rollover IRA conversions will now be dividend paying holdings to increase my cash flow out of the Roth.

I want to add a bit more info of what I did. A new post so not to get lost in the above.

About six years before I retired (I wasn't sure exactly when that was going to be at the time), I transferred my 401k into my Rollover IRA. Many might not agree with this decision, but my company had long stopped matching any contributions and the choices within the 401k plan weren't that great IMO. By transferring it, I was able to choose my own investments, which I'd been doing for many years in my taxable and Roth accounts. I don't claim to be an expert, but I did pretty well and at that time became more conservative in my choices, going for solid dividend growth companies. I have no regrets.

My first several years of IRA > Roth conversions were stocks that I expected to grow the best, regardless of their status....growth or income. The last two years I've moved only the biggest dividend paying stocks to add to my income/cash flow.

I also meant to mention, if you can, take advantage of any "make-up" amounts you can contribute to your Roth and 401k. IIRC, over 50 qualifies.

ETA:

"Catch-up contributions to retirement accounts like 401(k)s and IRAs are generally available for those age 50 and older at the end of the calendar year. In 2025, the catch-up contribution limit for individuals aged 50-59 is $7,500. Additionally, individuals aged 60-63 can contribute up to $11,250 as a catch-up contribution."

Should also consider the taxes on a surviving spouse who’ll only have half the deduction as a married couple. The Roth also can be bequeathed a bit more favorably especially if the kids are in high tax brackets. And tax free growth for the decade the kids have to spend it down.

quote:

Originally posted by Keystoner:
I'm putting $5,000 into the Roth account. This isn't complicated.

It is complicated to do a comparison of $5000 put into a 401k vs a ROTH.

The 401k has no taxes up front, so your cost of contributing is just that $5k.

The ROTH does have tax up front, so the cost of contributing is $5k plus the taxes.

You are specifying 2 different initial investments.

Let me try different numbers. $4k of your income is carved out for retirement savings. You have choices.

Your marginal tax rate today on your income is 25%.

You can put the entire $4k into a 401k because there is no tax on that carved out income.

Or, you can pay 25% tax on that income, leaving you with $3k to put into anything (gold bars under your mattress, simple savings account at your bank, etc). You choose ROTH.

Assume the rate of return and time cause the initial investments to double. Your 401k is now worth $8k, whereas your Roth is worth $6k.

But your $401k now gets taxed, so if the rate is 25% then your spendable remainder of the 401k will be $6k. The same as the Roth.

Vanguard doesn't care, and it's none of their business, what I pay in taxes. They get $5,000 in the Roth account and that's all they care about.

What I pay in taxes is reflected in the spreadsheet and it accounts for when it's paid.

The numbers are right.

quote:

Originally posted by Fly-Sig:

You are specifying 2 different initial investments.

No I'm not. I'm considering the EXACT same initial investment. That's crucial for the comparison. I'm also considering the EXACT same gross income.

quote:

Originally posted by Fly-Sig:

The 401k has no taxes up front, so your cost of contributing is just that $5k.

The ROTH does have tax up front, so the cost of contributing is $5k plus the taxes.

In order to contribute $5,000 to the Roth, I must have earned at least $6,666.67, and in order to contribute $5,000 to the 401(k), I must have earned at least only $5,000.

It's irrelevant.