How this number is made
A traditional contribution is pre-tax, so the whole gross amount is invested and the withdrawal is taxed. A Roth contribution is after tax, so less goes in and the withdrawal is not taxed. If the tax rate does not change, they match. The difference is the two rates.
- Use the marginal rates, not your effective rates.
- Growth is the same in both accounts. Fees would lower it.
Formula
Roth grows (gross × (1 − tax now)) for the years, untaxed at the end. Traditional grows the gross amount, then multiplies by (1 − tax later).
Worked example
With the figures already in the form, roth ahead of traditional, after tax is $0.
Questions
What about the income limits and the match?
Not here. A workplace match is a reason to contribute at least enough to get it, in whichever account the plan allows. Income limits can block a Roth IRA. This page is only the tax-timing math.
Why do equal rates tie?
Because multiplication commutes. Taxing before growth or after growth is the same if the rate is the same and the growth is the same.