Compare Roth and traditional IRA savings on an after-tax basis or calculate the break-even retirement tax rate using equal contributions or take-home cost.
Roth vs Traditional IRA Formula
This scenario model assumes fully deductible traditional IRA contributions and qualified Roth IRA withdrawals. It compares equal annual year-end deposits over a positive whole-number horizon, with identical constant returns. Existing balances, nondeductible basis, contribution eligibility and actual deduction amounts are not modeled.
For n whole annual contributions made at year-end, contribution growth is:
The traditional account after tax is:
The break-even future rate is:
Variables:
- C is the constant annual year-end contribution; the factor is n when r = 0
- r is annual return
- n is contribution years
- Tf is the retirement tax rate
Same-contribution mode deposits the same dollars into both accounts. Roth then has a higher current after-tax cost when the current income-tax rate is positive. Investing traditional tax savings outside the IRA is not included. Equal after-tax cost sets the traditional contribution to the entered Roth budget divided by (1 – current income-tax rate), assuming the entire contribution is deductible.
Equal contributions and equal after-tax cost answer different questions. For nonzero contributions, the break-even retirement rate is 0% in equal-contribution mode and the entered current rate in equal-cost mode. With zero contributions, every future tax rate ties; there is no unique threshold.
Eligibility, deductibility, income phaseouts and contribution limits must be checked separately. Deductibility can depend on workplace-plan coverage, modified adjusted gross income and filing status; a current tax rate alone does not establish it. See IRS Publication 590-A. If contributions are nondeductible, this fully deductible model is not the appropriate comparison.
Tax-Rate Comparison Guide
The first three rows below assume equal current after-tax cost, fully deductible traditional contributions, identical returns and qualified Roth withdrawals. They describe modeled balances, not recommendations. Equal nominal contributions have a different current cost.
| Tax pattern | Simplified tendency | Reason |
|---|---|---|
| Future rate higher | Higher modeled Roth value | Tax is paid at a lower current rate |
| Rates equal | Equal modeled values | Equivalent tax rate |
| Future rate lower | Higher modeled traditional value | Deduction occurs at the higher rate |
| Same nominal contribution | Roth often looks larger after tax | Roth has a higher current cost |
Example Problems
Example 1: Compare the same contribution.
As a hypothetical example, contribute $7,000 at each year-end for 32 years at a constant 7% return. The projected Roth value is $771,527.08; at a 22% retirement tax rate, fully deductible traditional contributions produce $601,791.12 after tax, a modeled difference of $169,735.96. Roth withdrawals are assumed qualified. Equal deposits do not have equal current costs; this example does not establish annual contribution eligibility.
Example 2: Compare the same take-home cost.
For a hypothetical $1,000 annual after-tax budget and a 20% current income-tax rate, fully deductible traditional contributions would be $1,250 per year. With equal returns and a 20% retirement rate, modeled after-tax values tie. Actual IRA limits, compensation and deductibility must be checked before applying the gross-up; it is not permission to exceed a contribution limit.
Frequently Asked Questions
Does the calculator enforce contribution limits?
No. Limits and catch-up amounts change, and eligibility can depend on income.
Why does the comparison basis matter?
The same nominal contribution does not create the same current take-home cost.
Are Roth withdrawals always tax-free?
The model assumes qualified Roth IRA withdrawals. Actual five-tax-year and distribution conditions still apply; retirement age alone does not establish qualification. See IRS Publication 590-B.
