[jaredsohn]

>If your tax rate will remain the same for withdraw as it does now, it doesn't really matter since the after tax value is the same whether you take out taxes now or later (i.e., tax_rate x (principal^gains) = (tax_rate x principal)^gains.

Assuming the money you invest goes up in value, aren't you better off in this scenario with a 401k over a Roth so that you can make gains on the money that would go toward taxes? You still have to pay taxes on the principal and the gains but compared to paying taxes on the money immediately, you're in effect borrowing money from the government at 0% to gamble with and keeping a portion of the return.

(Similarly, the expression tax_rate x (principal^gains) = (tax_rate x principal)^gains isn't true (beyond not being the right expression)).

.7 * (100000^1.07) != (.7 * 100000)^1.07 (assuming paying 30% in taxes and making 7% gains)

[berberous]

When people say it's the same, they are assuming you are investing the tax savings from using a traditional 401k. In other words, you could invest $10,000 in a Roth 401K, or $10,000 + ($10,000 * marginal tax rate) in a Traditional 401k. Then the numbers work.

[jaredsohn]

Another difference I just thought of (which may have been what I was originally thinking of but I said it wrong.)

I think an advantage of a Roth is that you don't have to pay tax on the money you earn via investing. For example, if your money in a Roth doubles then you only need to pay tax on the half of it that was there when you added money to the fund. Whereas for a traditional 401k you pay tax on money as it comes out which includes money earned via the investment.

[jaredsohn]

I made my prior (incorrect) analysis based on the math from this expression, despite saying the expression was wrong:

(i.e., tax_rate x (principal^gains) = (tax_rate x principal)^gains.

Gains should be multiplied rather than an exponential factor here. (I think this expression was created because gains are calculated as roughly (1+rate)^(number years) but at this higher level it should just be multiplied by the tax rate and the principal.