Originally posted by Rey HRH:
Keystoner
quote:
You’ve shown me my mission is stupid
I don't think your mission is stupid and I'm not patronizing. You're an engineer and you play with numbers. I do the same. Artists probably make pencil sketches and poets write verses.
quote:
The claim, which you say you’ve never heard, is stupid.
The claim isn't stupid. I backed into it as part of my analysis. And I even said, "So it appears the saying is true mathematically."
quote:
You changed the premise of the analysis, the black letter law of the claim. My original model compares equal contributions to a Roth and a 401(k).
This is a key divergence between the "claim" and your interpretation of the claim. It's not about "equal contributions to a Roth and a 401k;" it's about equal
out-of-pocket, net-of-tax contributions to a Roth and a 401k.
I am asking you to view the issue from a real world perspective: balancing retirement savings against immediate living expenses. You want to save as much as you reasonably can for retirement, while still covering your current and near-term expenses. The more you allocate toward retirement, the less you have for today's needs -- but the less you save, the more insecure your retirement could be. That's the fundamental tradeoff.
Let's assume you want $70,000 available for current, non-retirement spending from the income of $100,000.
* If you contribute $5,000 to a Roth IRA, you're doing so with after-tax dollars. Assuming a 25% effective tax rate, you'll pay $25,000 in taxes leaving you with $70,000 in spendable income. Your out-of-pocket contribution is the full $5,000 - it came from money that would have went into your pocket and could have otherwise spent.
* If instead you contribute $5,000 to a traditional 401(k), that contribution is pre-tax. Your taxable income drops to $95,000, so your tax bill is reduced to $23,750. That leaves you with $71,250 for spending. Because you still have $1,250 more in spendable money in your pocket than in the Roth scenario, your
real out-of-pocket cost for the 401(k) contribution is only $3,750.
So while the contribution amounts may look equal on paper, the
cost to you -- in terms of money you can't spend today -- is not equal. That's what "equal out-of-pocket, net-of-tax contributions is getting at.
* To get an "equal out-of-pocket, net-of-tax contribution amount, you would need to contribute $6,666.67 to the 401(k). That reduces your taxable income to $93,333.33 at a 25% tax rate, your tax bill is $23,333.33 -- leaving you with $70,000 in your pocket as spendable income, just like in the Roth scenario.
So even though you're giving up the same $5,000 of current spending income in both cases, the 401(k) ends up with $6,666.67, while the Roth has only $5,000. That's why it's misleading to compare equal contribution amounts without adjusting for taxes - the real cost to you isn't the same.
The reason I lay it out this way is because this is the
correct interpretation of the claim. When you compare the net future value of both accounts -- using
equal-out-of-pocket, net-of-tax contributions -- the results align perfectly with the claim.
* A $6,666.67 contribution to a 401(k) compounds to $301,728.37. A 25% tax is $75,432.09 leaving you with a net of $226,296.28.
* A $5,000 Roth contribution (same out-of-pocket cost) compounds to $226,296.28 - with no taxes due. So both paths result in the same net retirement value, despite different contribution amounts - precisely because they started with the same real cost to you today.
And because this approach achieves the claim -- if the tax is the same in the future, a 401(k) is the same as a Roth IRA -- it serves as proof that the reasoning is sound. Q.E.D.