Retirement accounts / tax treatment

Roth vs traditional IRA

Compare a Roth and a traditional IRA on equal out-of-pocket cost, so the only remaining variable is the tax rate you face today versus the one you will face at withdrawal.

WinnerTraditionalTax today24.0%Tax at withdrawal22.0%

Roth after-tax value

$474,368

Contributions taxed now, growth never taxed

Traditional after-tax

$486,851

Pre-tax $624,168 taxed at 22.0%

Traditional advantage

$12,483

Traditional wins at these tax rates

Break-even tax rate

24.0%

Retirement rate at which the two tie

Year-by-year comparison

Roth (after-tax contributions) against traditional (pre-tax contributions of equal out-of-pocket cost).

25 years

Year-by-year comparison
Year	Roth balance	Traditional pre-tax	Traditional after tax
Year 1	$7,500	$9,868	$7,697
Year 2	$15,525	$20,428	$15,934
Year 3	$24,112	$31,726	$24,746
Year 4	$33,300	$43,815	$34,176
Year 5	$43,131	$56,751	$44,266
Year 6	$53,650	$70,592	$55,062
Year 7	$64,905	$85,402	$66,613
Year 8	$76,949	$101,248	$78,973
Year 9	$89,835	$118,204	$92,199
Year 10	$103,623	$136,347	$106,350

The traditional column grows faster before tax because more money went in — the question is whether the withdrawal tax rate is lower than today’s.

After-tax value over time

The gap widens with the horizon, but its sign depends only on the two tax rates.

Where the money ends up

Roth value against traditional pre-tax and after-tax value.

Canonical equations

The exact relationships implemented by this engine.

FV = C·((1+r)ⁿ − 1)/r · contributions at year end

FV_R = FV(C, r, n) · no tax on qualified withdrawals

FV_T = FV(C/(1−t₀), r, n)·(1−t₁) · grossed up for equal out-of-pocket cost

t₁* = t₀ · equal cost comparison ties at equal tax rates

Show model notation and computationOpen the symbolic form, the variable definitions, and the step-by-step derivation when you need the detail.

A clear path from inputs to results.

The Roth versus traditional question reduces to one comparison: your marginal tax rate today against your marginal rate when you withdraw. To see that clearly, both accounts must be funded with the same amount of after-tax money — otherwise the comparison is rigged by the contribution size.

Step-by-step methodWorked exampleAssumptions explained

How to use

Enter the annual contribution in after-tax dollars.

Set the years to retirement and an expected return.

Enter your marginal tax rate today and your expected rate at withdrawal.

Read both after-tax outcomes: the traditional contribution is grossed up so the out-of-pocket cost matches.

Check the break-even rate — with equal cost, the two tie exactly when the rates are equal.

Use the sensitivity chart to see how the answer flips as the retirement rate changes.

The formula

FV = C\frac{(1+r)^n - 1}{r}, \qquad \text{Roth}: FV_R = FV(C), \qquad \text{Traditional}: FV_T = FV\!\left(\frac{C}{1-t_0}\right)(1-t_1)

Reference: IRC §408A (Roth IRA); standard tax-deferred equivalence argument.

Worked example

$7,500 a year for 25 years at 7% (default inputs)

Inputs

Annual after-tax contribution $7,500 (the 2026 IRA limit).
25 years at 7%.
Marginal tax rate today 24%; expected rate at withdrawal 22%.

Calculation path

1
Roth future value: 7,500 × ((1.07^25 − 1) / 0.07) = $474,368, all tax-free.
2
Equal-cost traditional contribution: 7,500 / (1 − 0.24) = $9,868 pre-tax.
3
Traditional future value: 9,868 × ((1.07^25 − 1) / 0.07) = $624,168.
4
After 22% withdrawal tax: 624,168 × 0.78 = $486,851.
5
Traditional wins by $12,483 because the withdrawal rate is lower than today’s rate.

Result

Roth $474,368 after tax · traditional $486,851 after tax · traditional ahead by $12,483.

Interpreting the result

The traditional account wins here only because the assumed withdrawal rate is two points lower than today’s. Reverse the two rates and the Roth wins by a similar margin. The break-even is exactly the current rate: with equal out-of-pocket cost, the accounts tie when t₁ = t₀. Everything else is a bet on your future tax bracket.

Assumptions & limitations

A constant marginal tax rate applies to contributions and withdrawals. Progressive brackets make the real answer path-dependent.

Both accounts earn the same return. In practice you can hold different assets in each.

No required minimum distributions. Traditional IRAs force withdrawals from age 73; Roth IRAs do not during the owner’s lifetime.

Contribution limits are not binding. At $7,500 a year this is the 2026 IRA limit; a 401(k) would allow more.

State taxes, early-withdrawal penalties and the five-year rule are excluded.

Frequently asked questions

Which is better, Roth or traditional?

If your tax rate will be lower in retirement, traditional wins. If it will be higher, Roth wins. If they are equal, they tie on pure arithmetic — and the tie-breaker becomes RMDs, estate planning and tax diversification.

Do Roth IRAs have required minimum distributions?

Not for the original owner. Traditional IRAs require withdrawals from age 73, which can force income into a higher bracket late in life. That asymmetry favours Roth for people with large balances.

What about a backdoor Roth?

A non-deductible traditional contribution converted to Roth. It works but interacts with the pro-rata rule if you hold other traditional IRA balances, so the conversion can be partly taxable.

Why gross up the traditional contribution?

Because $7,500 of after-tax money can fund $9,868 of pre-tax deferral when your rate is 24%. Comparing $7,500 of Roth against $7,500 of traditional would understate the traditional account by the tax you did not pay.

Can I contribute to both?

Yes, but the annual limit is shared across all IRAs. The split is a tax-diversification decision rather than a doubling of the limit.

Does the Roth five-year rule matter?

Yes for withdrawals of earnings. Contributions can be withdrawn at any time tax-free; earnings need the account to be five years old and the owner to be 59½ for tax-free treatment.