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Traditional or Roth: 10,000 before tax for 30 years at a 22 % tax rate now and 15 % in retirement

Tool	Traditional versus Roth
Source	Closed-form compound growth applied to the general rules of Internal Revenue Service (2026), Publication 590-A, Contributions to Individual Retirement Arrangements (IRAs), and Publication 590-B, Distributions from Individual Retirement Arrangements (IRAs), for use in preparing 2025 returns (Roth contributions are not deductible and qualified Roth distributions are tax free; Traditional distributions of deductible contributions are fully taxable). The case is illustrative, not a printed example; both tax rates are example entries.
Level	Undergraduate

Problem

A saver can set aside 10,000 of pay before income tax and will withdraw it in 30 years. The expected return is 6 % a year. The tax rate on the last dollars earned is 22 % now and is assumed to be 15 % in retirement. Find what a Traditional account and a Roth account each leave after tax, the difference, and the retirement tax rate at which the two are equal.

Inputs to Enter

Amount before tax 10,000; years to withdrawal 30; annual return 6 %
Tax rate now 22 %; retirement tax rate 15 % (Simple mode)

Open the Traditional versus Roth tool (loaded with this example)

Answers

Growth of 1 over 30 years: F = 1.06^30 = 5.7435
Traditional: 10,000 × 5.7435 × (1 − 0.15) = 48,819.67 after tax
Roth: contribution after tax 10,000 × (1 − 0.22) = 7,800.00; 7,800 × 5.7435 = 44,799.23, withdrawn tax free
Ratio Traditional / Roth = (1 − 0.15) / (1 − 0.22) = 1.0897: the return and the years cancel
Difference 48,819.67 − 44,799.23 = 4,020.44, or 8.97 % of the Roth result
Break-even retirement tax rate = the tax rate now, 22 %: at 22 % both leave 44,799.23; at 25 % the Roth leaves 1,723 more
Advanced default, converting a 50,000 balance with the tax paid from outside money (15 % tax drag): not converting 293,016.99, converting 287,174.56, equal at a retirement rate of 17.03 %

Notes

The tool's default inputs are this case; press Submit. The result turns on the retirement tax rate, which nobody knows in advance; the page tabulates rates from 0 to 40 %. Contribution and income limits change every year and are not checked (see IRS Publication 590-A). Every number was checked against an independent year-by-year numpy model with scipy root finding (test_traditional_vs_roth.php). An illustration, not tax advice. A calculator for education and analysis, not investment advice.