Equal tax rates vs balance of tIRA/Roth IRA

[Time2]

I watched this short,

it concludes, a Roth ends with a higher balance, even with the same contribution. He shows 3 examples in the original from a Voya calculator. All show the Roth better. I'd like to correct it (someone tried) but I'm not sure what it is calculating and I think it misses the tax that you save that could/should be invested.
Does anyone have a good argument about tIRA vs Roth with equal tax rates, or a page with numbers to prove the arguement?
What am I missing that makes the Roth look so much better or what is the calculator missing.



Here's the longer version, 9 minutes.

 

[pb4uski]

No, if the tax rate is the same then a Roth does not come out ahead all else being equal.

Let's take a hypothetical couple whose tax rate is 22%.

If they invest $10k annually in a Roth for 30 years and the account earns 5% then at the end of 30 years the balance is $664,388.48 [=FV(5%,30,-10000)].

The $10k annually would be $12,820.51 pre-tax [(10000/(1-22%)] so with the Roth they are paying taxes on $12,820.51 of income or $2,820.51 in taxes for a net cash flow of $10,000 used to make the annual ROTH contributions.

If they invest $12,820.51 annually in a traditional IRA for 30 years and the account earns 5% then at the end of 30 years the balance is $851,780.10 [=FV(5%,30,-10000/(1-22%))]. They avoid having to pay income tax on that $12,820.51 annually.

The $851,780.10 if withdrawn would have an after-tax value of $664,388.47 [$851,780.10*(1-22%)]

 

[Time2]

No, if the tax rate is the same then a Roth does not come out ahead all else being equal.

Right! I think you are disagreeing with the video conclusion, not me.

Let's take a hypothetical couple whose tax rate is 22%.

If they invest $10k annually in a Roth for 30 years and the account earns 5% then at the end of 30 years the balance is $664,388.48 [=FV(5%,30,-10000)].

The $10k annually would be $12,820.51 pre-tax [(10000/(1-22%)]

If they invest $12,820.51 annually in a traditional IRA for 30 years and the account earns 5% then at the end of 30 years the balance is $851,780.10 [=FV(5%,30,-10000/(1-22%))].

The $851,780.10 would have an after-tax value of $664,388.47 [$851,780.10*(1-22%)]

Thanks for the math. What do you think the Voyavcalculator is doing different?

 

[pb4uski]

I don't think it is doing much different. I found the VOYA calculator and input $5k a year contribution for 30 years at 5% (VOYA said that $10k a year was too much but it wouldn't be too much for a couple). Anyway, if I input age 30, retiring at 60, $5k annual contrbutions, 5% return and 22% now and 22% later then the VOYA returns $348,804 for the Roth and $335,106 for a tIRA so a very slight difference.

I suspect that the reason that he got such high savings is that the current tax rate was much higher than the retirement tax rate, which is the default, and he didn't realize it... I had to change them to be equal.

https://www.voya.com/tool/roth-ira-calculator