<prompt> Human: Ive seen lots of discussion recently about Roth vs. Traditional IRA. And a lot of it is wrong. Roth vs. TraditionalMany people in rpf choose a Roth IRA over a Traditional IRA for very good reasons: liquidity before retirement, no forced distributions, backdoor contributions for high-earners, etc. However, theres a lot of people who propose mathematical reasons for choosing Roth over Traditional, meaning they believe you will have more money in retirement if you select a Roth.Everyone knows that the Roth vs. Traditional choice is mainly influenced by what your current tax rate is and what you think your tax rate will be in retirement. But Ive seen some very surprising comments claiming that your current age is more important than your future tax rate. The supposed benefit of a Roth is something like if youre young, you get decades worth of compounded growth, with no taxes at the end; but if you choose a Traditional IRA, you have to pay regular income taxes on all that growth. Unfortunately, this thinking is just wrong. If you ignore the difference between present and future tax rates, a Traditional IRA is almost certainly mathematically superior to a Roth IRA. Lets talk about why. Lets Do Some MathTo make things simple, lets consider a person who makes 60,000 of taxable income a year. This person is young, 30 years from retirement. They will make an average of 7 a year in the stock market. When they retire, they will withdraw 60,000 a year the same amount they make now. For simplicity, lets also ignore inflation and assume tax rates stay constant. This persons current and future tax rates will be exactly the same: a marginal tax rate of 25, an effective tax rate of 18.1, and a capital gains tax rate of 15. He has 5,500 pretax dollars to contribute to either a Roth IRA or a Traditional IRA. What could that 5,500 look like in 30 years? Traditional Roth---------Contribution pretax dollars 5,500 5,500Tax on Contribution 0 1,375 25Starting Balance 5,500 4,125Ending Balance 7 for 30 years 41,867.40 31,400.55Tax on Distribution 7,578 18.1 0Total Distribution 34,289.40 31,400.55After 30 years, our retiree could have almost 3,000 about 9 more if he had chosen a Traditional IRA. And thats just on this years contribution; our earner would be contributing 5,500 each year.So, what the hell? How does this work out? The Traditional IRA ends up with more money because the distributions are taxed at the effective tax rate, but the Roth contributions come from money taxed at the marginal tax rate. Our retirees distributions are taxed at his effective rate because the majority of his income will come from his tax-advantaged accounts. Wait a second here...I can hear you now: But if I contribute 5,500 to a Roth, my starting balance is 5,500, not 4,125! Youre right, but remember: our earner was contributing 5,500 of pretax money. The problem changes a little bit if our earner wants to contribute 5,500 of after-tax money to his Roth. 5,500 in after-tax money is equal to 7,333.33 pretax money 5,500 1 ndash; 25.So, lets assume our earner has 7,333.33 pretax dollars to contribute to either a Traditional or Roth. He cant contribute more than 5,500 to a Traditional, so he has to put the remainder into a taxable investment account. Lets assume his investments in this account make the same 7 a year for 30 years. Now certainly a Roth is the better choice, right? Right...? Traditional Taxable Roth---------------Contribution pretax dollars 5,500 1,833.33 7,333.33Tax on Contribution 0 458.33 25 1,833.33 25Starting Balance 5,500 1,375 5,500Ending Balance 7 for 30 years 41,867.40 10,466.85 41,867.40Tax on Distribution 7,578 18.1 1,363.78 15 of gains 0Total Distribution 34,289.40 9,103.07 41,867.40So, in this retirement scenario, you will have 41,867 if you went with the Roth, but you will have 43,392 if you went with the Traditional Taxable; thats about 3.5 more! The Roth still doesnt give you more than the Traditional. So, what does this mean?It means that if you ignore the difference between your current and future tax rate, the Traditional IRA is usually the mathematically optimal choice. This discounts the other benefits of a Roth IRA like pre-retirement withdrawal of contributions; the value of these benefits depends on the investor. I hope this sets the record straight regarding how age affects the Roth or Traditional decision. Both types can benefit from decades of compounded growth; but the tax-free benefit of the Roth IRA is cancelled out by the fact that the pretax money contributed to a Traditional is worth more than after-tax money. Roth or Traditional?As always, the biggest factor in the Roth or Traditional question is your current tax rate versus your retirement tax rate. Theres actually a formula for comparing your current marginal rate with your future effective rate. future_effective gt; 1 ndash; 1 1 current_marginalIf you think your future effective tax rate will be greater than the result of that formula, then you should choose a Roth IRA. For instance, if your current marginal tax rate is 25, you should choose a Roth if your future effective tax rate is greater than 20. See this page for more information about this formula.Thats the mathematical solution. But in reality, you should carefully consider the additional benefits of a Roth IRA when deciding.  <response>: British person only reading this because I was curious as to what sort of Republican Dissident a ROTH was. 