Direct Answer

In the simplest equal-pre-tax-cost model, Roth and deductible Traditional outcomes break even when the marginal tax rate paid on the Roth contribution today equals the marginal tax rate paid on the Traditional withdrawal later. Time and investment return multiply both sides. Real-world results can diverge because IRA contribution caps, Traditional deduction eligibility, state tax, required minimum distributions, basis, and the treatment of Traditional tax savings break the simple symmetry.

The Core Formula

Let:

• P = pre-tax household dollars available;
• t_now = marginal tax rate now;
• t_future = marginal tax rate on future Traditional withdrawals;
• r = annual investment return;
• n = years invested.

Roth future value

FV_Roth = P × (1 − t_now) × (1 + r)^n

The Roth contribution is made with after-tax dollars, so the tax cost is applied first, before compounding.

Traditional after-tax future value

FV_Trad = P × (1 + r)^n × (1 − t_future)

The Traditional contribution grows at the full pre-tax amount, but the tax cost is applied at withdrawal.

The break-even condition

When t_now = t_future, the two expressions are equal in this simplified model. That is because the same tax factor is multiplied either before or after the same growth factor. The order of multiplication does not create a free advantage when the rates are identical.

Why "Roth Grows Tax-Free" Does Not by Itself Prove Roth Wins

Qualified Roth withdrawals can be tax-free. The contribution, however, is made with after-tax dollars.

A deductible Traditional contribution defers the tax until distribution.

If the same tax rate applies at both ends, the order of multiplication does not create a free advantage. The decisive tax variable is the rate difference between what is paid now and what will be paid later.

Break-Even Rule

Ignoring other factors:

• t_now < t_future: Roth has the tax-rate advantage. Paying tax now at the lower rate and growing the full amount tax-free produces a better outcome.
• t_now > t_future: Deductible Traditional has the tax-rate advantage. Deferring the higher-rate tax to a lower-rate withdrawal is more favorable.
• t_now = t_future: Pure tax timing breaks even. Other factors, such as required minimum distributions, estate treatment, and contribution-cap mechanics, decide the outcome.

How the Contribution Cap Changes Practical Comparisons

For 2026, the combined IRA contribution cap is $7,500, or $8,600 at age 50+. See IRS: IRA Contribution Limits.

A household that maxes a Roth puts the full legal contribution into the after-tax retirement wrapper, paying taxes with outside cash.

A household that maxes a deductible Traditional IRA puts the same nominal contribution into a pre-tax wrapper and receives tax savings outside the account.

Therefore two comparison modes are useful:

Equal-contribution mode

"What happens if I put $7,500 into either account?"

In this mode, both accounts receive the same dollar amount. Roth receives after-tax dollars; Traditional receives pre-tax dollars that will be taxed on withdrawal. Equal contributions do not represent equal pre-tax economic cost.

Equal-household-cost mode

"What happens if the household devotes the same pre-tax economic resources to either strategy?"

This mode should include the Traditional tax savings invested alongside the contribution. If the tax savings are spent rather than invested, the household has effectively saved less for retirement than the equal-cost framing implies.

Traditional Deduction-Savings Formula

If a $7,500 Traditional IRA contribution is fully deductible and the affected marginal rate is 24%:

Current tax savings ≈ $7,500 × 0.24 = $1,800

If those $1,800 of savings are invested, they belong in the Traditional strategy's future-value calculation. If they are spent, the household has effectively saved less for retirement, and the Traditional strategy's compounding advantage is reduced accordingly.

Do not assign this tax saving if the contribution is nondeductible. Verify deduction eligibility under IRS Publication 590-A.

Worked Examples

Example 1: Same rate now and later (break-even)

Assume:

• P = $10,000;
• t_now = 22%;
• t_future = 22%;
• r = 7%;
• n = 30.

Roth begins with:

$10,000 × 0.78 = $7,800

Traditional begins with the full pre-tax $10,000 equivalent but loses 22% when withdrawn. Because both use the same growth factor and the same tax factor, the simplified after-tax future value is equal. Neither account has a tax-rate advantage.

Example 2: 22% now and 32% later (Roth advantage)

Roth future value:

P × 0.78 × (1 + r)^n

Traditional after-tax future value:

P × (1 + r)^n × 0.68

Roth has the rate advantage because the current tax price (22%) is lower than the future tax price (32%). Paying 22% now on a dollar that grows untaxed is better than growing the full dollar and paying 32% on withdrawal.

Example 3: 32% now and 22% later (Traditional advantage)

Roth future value:

P × 0.68 × (1 + r)^n

Traditional after-tax future value:

P × (1 + r)^n × 0.78

A deductible Traditional contribution has the rate advantage because the deduction occurs at the higher rate (32%) and the withdrawal is taxed at the lower rate (22%). Deferring tax from 32% to 22% produces a better after-tax outcome.

Adding State Tax

A more complete model compares combined marginal tax cost now and later. At an educational approximation level:

t_now_total  ≈ federal_now  + state_now
t_future_total ≈ federal_future + state_future

Exact state/federal interactions can be more complicated. Some states exempt all retirement income; others tax it the same as wages. Partial exemptions and state-specific phase-outs add further complexity. Label any model that uses this approximation accordingly rather than presenting the result as a precise combined rate.

A move from a high-income-tax state during working years to a no-income-tax state in retirement can shift the effective rate spread materially in favor of a Traditional contribution. The reverse shift also occurs and is worth modeling where applicable.

Factors the Simple Formula Does Not Capture

The core formula isolates the tax-rate timing effect. The following factors can change the real-world result and belong in scenario analysis rather than inside a single-number answer:

• Roth MAGI phase-outs that reduce or eliminate direct Roth contribution eligibility;
• Traditional deduction phase-outs for workplace-plan participants;
• partial deductions that change the effective upfront tax benefit;
• nondeductible basis and Form 8606 tracking requirements;
• conversion tax on Roth conversions from existing Traditional balances;
• IRA contribution caps that limit the amount eligible for either wrapper;
• required minimum distribution timing beginning at age 73, which forces taxable income from Traditional accounts regardless of need;
• Social Security income taxation interactions that can increase effective marginal rates at certain income thresholds;
• Medicare income-related monthly adjustment amounts (IRMAA) triggered by high modified adjusted gross income;
• taxes on a taxable side account holding Traditional tax savings, which reduce the compounding advantage if savings are invested in a taxable brokerage;
• estate or survivor goals that favor Roth accounts because inherited Roth IRAs can extend tax-free growth under applicable rules;
• early-access flexibility, since Roth contributions (not earnings) can be withdrawn penalty-free before 59½;
• future legislation that changes rates, brackets, or account rules.

Educational formula only. Actual taxes can differ because of deductions, credits, surtaxes, state rules, and other income interactions. Verify current rules with a qualified tax professional.

References

1. IRS: Retirement Topics - IRA Contribution Limits. Accessed 2026-09-05.
2. IRS: Publication 590-A, Contributions to Individual Retirement Arrangements. Accessed 2026-09-05.
3. IRS: Publication 590-B, Distributions from Individual Retirement Arrangements. Accessed 2026-09-05.
4. Swoopr: Roth vs Traditional Calculator.