Compound Interest Calculator (US — IRS, 2026 IRA, 401(k), Roth)

Most US compound interest calculators model a single pre-tax compounding path and ignore the IRS wrapper decision that drives 20-40% of the terminal value across multi-decade horizons. This page projects three wrappers in parallel — Roth (tax-free), Traditional (tax-deferred), and taxable brokerage — using 2026 IRS contribution limits, the federal marginal tax brackets that determine which wrapper wins for your income trajectory, and the SECURE 2.0 rules on RMDs and catch-up contributions.

Why the IRS wrapper matters more than the rate of return

The headline assumption in any US retirement plan is the rate of return. That assumption is usually wrong in both directions — the long-run figure is reasonably well-known (~7% real for US equities since 1928 per the NYU Stern Damodaran database, ~10% nominal before inflation), but the spread of 10-year forward returns around that average is enormous, and the future is genuinely unknown. The wrapper decision is different: the rules are written in the Internal Revenue Code, the tax math is deterministic once the inputs are fixed, and the impact on terminal value is comparable in magnitude to a one-or-two-percentage-point return swing over a 30-year horizon.

The same $100/month contribution at 7% over 40 years lands at very different terminal values depending on which wrapper holds the dollars. In a Roth IRA the contribution is post-tax (you paid the tax going in at your contribution-year marginal rate) and the growth compounds tax-free with no tax on qualified withdrawal. In a Traditional IRA the contribution is pre-tax (deductible up to certain income limits if you're also covered by an employer retirement plan), the growth compounds tax-deferred, and the entire balance is taxed as ordinary income on withdrawal at the retirement-year marginal rate. In a taxable brokerage account the contribution is post-tax, dividends are taxed annually (qualified dividends at 0%, 15%, or 20% federal depending on income, ordinary dividends at marginal rate), and capital gains are taxed on realisation at long-term rates (0%, 15%, 20%) plus the 3.8% Net Investment Income Tax for high earners, plus state.

The aggregate annual tax drag on a typical taxable brokerage holding — a buy-and-hold equity index fund with qualified dividend reinvestment and minimal turnover — runs at roughly 0.5-1.5 percentage points off the gross return, with the high end of that range covering accounts that rebalance frequently and the low end covering ETFs with low turnover and qualified dividends only. That sounds small in any given year. Compounded over 30-40 years it is not.

2026 IRS contribution limits and key thresholds

The IRS publishes annual cost-of-living adjustments to retirement contribution limits each November via an IRS Notice. The 2026 figures will be released in late 2025 and may move modestly from the 2025 baseline. The 2025 limits and the approximate 2026 indexed figures are:

• 401(k) employee elective deferral: $23,500 (2025), approximately $24,000 (2026 indexed)
• 401(k) catch-up (age 50+): $7,500 unchanged
• SECURE 2.0 super catch-up (ages 60-63): $11,250 — the higher of $10,000 or 150% of the regular catch-up, indexed
• IRA / Roth IRA contribution: $7,000 with a $1,000 catch-up for 50+, total $8,000 for 50+
• Roth IRA income phase-out (2025): single $150,000-$165,000, married filing jointly $236,000-$246,000 — both modestly higher in 2026 with indexing
• 401(k) total annual additions cap (employee + employer + after-tax): $70,000 (2025), approximately $71,000 (2026 indexed)
• HSA family contribution: $8,550 (2025), approximately $8,750 (2026 indexed); single coverage approximately $4,300 (2025)
• HSA catch-up (age 55+): $1,000 unchanged

The Roth IRA income phase-out is the most common surprise for high earners. A married couple filing jointly with a combined modified AGI of $260,000 cannot contribute directly to a Roth IRA — the contribution limit phases out between $236,000 and $246,000 of MAGI and is fully eliminated above $246,000. The Backdoor Roth (a non-deductible Traditional IRA contribution followed by an immediate Roth conversion) circumvents the income limit and is widely used by high-income households, with the caveat that the pro-rata rule applies if you already hold pre-tax Traditional IRA balances elsewhere — in that case the conversion is taxable on a pro-rata basis between the after-tax and pre-tax slices of your aggregate IRA balance.

The math — pre-tax vs post-tax vs taxable

The compound formula with monthly contributions is FV = P(1 + r/n)nt + PMT × [((1 + r/n)nt − 1) ÷ (r/n)], compounded monthly. The Roth case uses the full nominal return; the Traditional case applies the withdrawal tax to the terminal balance; the taxable case applies an annual tax drag to the compounding rate so that the cost of taxation reinvests forever and compounds against you.

Three worked examples at the IRA contribution limit illustrate the gap. A $7,000 annual contribution at 7% for 30 years (computed annually for transparency; the calculator runs monthly compounding for greater precision) compounds to $661,226 in a Roth IRA — the future-value-of-an-annuity figure, $7,000 × ((1.07³⁰ − 1) ÷ 0.07), withdrawn tax-free.

The same $7,000 annual contribution in a Traditional IRA also compounds to $661,226 pre-tax over 30 years. Withdrawing the full balance in retirement at a 22% federal marginal rate leaves $515,756 net. Compared to the Roth, the Traditional underperforms by $145,470 on the contribution-equal basis — a 22% shortfall — because the Roth's full balance flows out tax-free while the Traditional surrenders 22% to ordinary income tax at withdrawal.

The fair pre-tax-equivalent comparison narrows the gap considerably. The Traditional contributor whose 24% contribution-year marginal rate produces a $1,680/year tax saving on the $7,000 deduction can reinvest those tax savings into a taxable side-pot. Compounded at 5% effective (i.e., 7% nominal less a ~28% annual tax drag from qualified dividends and capital-gains turnover) for 30 years, the side-pot reaches roughly $111,617. Add that to the $515,756 net Traditional balance and the comparable Traditional total is around $627,373, against the Roth's $661,226. The Roth wins by approximately $33,853 in this fair comparison — a 5% advantage rather than 22%.

The third wrapper — taxable brokerage — faces the heaviest drag, and the magnitude depends on how aggressively the account churns. At one extreme, a high-turnover taxable portfolio paying tax at the contribution-year marginal rate on a high fraction of returns each year (the "28% blended drag" assumption: 7% × (1 − 0.28) = 5.04% effective) compounds $7,000 per year to roughly $468,279 over 30 years. At the other extreme, the calculator's default model — a long-term buy-and-hold portfolio with qualified dividends and modest realisation (0.6 × contribution-year marginal rate annual drag, i.e., a 24% bracket investor pays effective drag of 14.4% on returns) — lifts the taxable terminal balance toward $580,000 at the $583/month default. Either way, the taxable account loses to the Roth by 15-30% across the realistic range of tax-drag assumptions, precisely because the tax compounds annually rather than being assessed once at withdrawal.

The decision rule that emerges from these three numbers: the Roth wins decisively for a typical retiree who stays in the same or a lower bracket from contribution-year to retirement-year; the Traditional wins for a high earner currently in the 32-37% bracket who expects to retire in the 22%- bracket; the taxable account loses in every reasonable scenario but is the only wrapper available once IRS limits are exhausted, which is why high earners frequently hold all three in parallel.

RMDs — when the tax-deferred account starts taxing back

Required Minimum Distributions are the structural reset that hits Traditional balances starting at age 73 under current law, rising to age 75 from 2033 under the SECURE 2.0 Act. The first-year RMD is computed by dividing the prior-year December 31 account balance by the IRS Uniform Lifetime Table divisor for your age. At age 73 the divisor is 26.5; at age 80 it falls to 20.2; at age 90 it's 12.2. The divisor is published in IRS Publication 590-B Appendix B.

A $1,000,000 Traditional IRA balance at age 73 produces a year-1 RMD of $1,000,000 ÷ 26.5 = $37,736, taxed as ordinary income at the retiree's marginal rate. The IRS Uniform Lifetime Table is constructed so that the divisor approximates the retiree's remaining life expectancy plus a small buffer, but it materially accelerates withdrawal in later years — a 90-year-old with $1M still has to withdraw $1,000,000 ÷ 12.2 = $81,967 in that year, taxed as ordinary income. RMDs do not apply to Roth IRAs during the original owner's lifetime, and SECURE 2.0 eliminated the prior RMD requirement on Roth 401(k) balances for tax years from 2024 onwards.

For high-balance Traditional holders, the RMD schedule can push retirees from a lower bracket back into a higher one in their late 70s and 80s, undoing some of the tax arbitrage that drove the Traditional decision in the first place. The strategic response is the Roth Conversion ladder: convert chunks of Traditional balance to Roth in the early-retirement years between actual retirement (commonly age 60-67) and the RMD trigger (age 73-75), paying the federal tax now at a known marginal rate rather than accepting the political-risk exposure of future rate changes plus the RMD-driven bracket creep.

Tax-bracket arbitrage over a 30-year career

The strongest case for Traditional contributions is the spread between your contribution-year marginal rate and your withdrawal-year marginal rate. The contribution deduction is taken at the higher rate; the withdrawal is taxed at the lower rate; and the difference compounds across the contribution years. A worked example illustrates the magnitude.

Contribute $20,000 per year to a Traditional 401(k) at a 24% marginal rate for 20 years. The cumulative federal tax saved on the deductions is $20,000 × 0.24 × 20 = $96,000, available as cash to invest in a taxable side-pot. The underlying $20,000/year compounds at 6% real inside the 401(k) for 20 years to reach approximately $735,000 pre-tax. A 22% withdrawal tax leaves $573,300 net. Meanwhile the side-pot compounds at 5% effective (6% real less ~1pp annual drag) for the same 20 years and reaches approximately $159,400.

The Traditional + side-pot total is around $732,700. Compare against a Roth that contributed the same $20,000 post-tax for 20 years at 6%: it reaches the same $735,000, fully tax-free, but required $26,316/year of pre-tax income to fund the $20,000 contribution at the 24% rate (the gov collected $6,316/year of tax that the Traditional borrower deferred). On a pre-tax-equivalent basis the Traditional wins because of the bracket arbitrage; on a contribution-equal basis the Roth wins because the contribution-year tax was never paid. The 2-percentage-point spread between contribution-year and withdrawal-year tax is the structural Traditional advantage, and it scales linearly with the spread — a 32% contribution rate vs 22% retirement rate (a 10-point spread) widens the Traditional advantage substantially.

The Mega Backdoor Roth (advanced)

The Mega Backdoor Roth is the contribution strategy for high earners with access to a 401(k) plan that permits after-tax (non-Roth, non-deductible) contributions and in-plan Roth conversions or in-service rollovers. The mechanism: contribute up to the 401(k) total annual additions limit (approximately $70,000-$71,000 in 2026) using a combination of regular pre-tax or Roth contributions ($23,500), employer match, and after-tax contributions, then immediately convert the after-tax portion to Roth before significant earnings accrue inside the after-tax bucket.

For an employee with no employer match, the Mega Backdoor capacity is roughly $70,000 − $23,500 = $46,500 per year of additional Roth contribution, which is materially larger than the standard Roth IRA $7,000 cap. The income phase-out that blocks Roth IRA contributions for high earners does not apply to the in-plan conversion, which makes the Mega Backdoor the cleanest way for households over the Roth IRA income limit to access Roth growth at scale.

The catch is that only a fraction of US 401(k) plans permit the mechanism. The plan's Summary Plan Description (SPD) must explicitly allow both after-tax contributions and either in-plan Roth conversions or in-service rollovers to a Roth IRA. Plans that allow one but not the other create a less-efficient version of the strategy where after-tax dollars sit inside the 401(k) accruing taxable earnings on the pre-conversion balance — better than nothing but materially worse than the immediate-conversion playbook.

State income tax drag

Forty-one US states tax IRA and 401(k) withdrawals at the resident state's marginal rate at retirement. Nine states have no broad income tax: Alaska, Florida, Nevada, New Hampshire (interest and dividends only, fully phased out by 2027), South Dakota, Tennessee, Texas, Washington, and Wyoming. State tax does not affect the federal treatment, but it materially changes the net withdrawal. A $100,000 Traditional withdrawal at the 22% federal bracket leaves $78,000 net in Texas, against approximately $70,700 net in California (where the top combined federal-and-state rate on retirement income runs around 29.3%).

The state-tax drag is the strongest case for the Roth Conversion ladder strategy in high-tax states (California, New York, Oregon, Minnesota, New Jersey). Convert chunks of Traditional balance to Roth in lower-bracket years before retirement, paying the federal-and-state tax now at a known rate, rather than accept the political-risk exposure of unknown future rates plus the RMD-driven bracket creep. The same calculus works in reverse for retirees who plan to relocate from a high-tax to a no-tax state: hold the Traditional balance through the high-tax-state years, retire to Texas or Florida, and withdraw at the federal-only rate.

Calculator inputs and outputs

This calculator takes eight inputs: starting balance, monthly contribution, expected nominal annual return (default 7% per the long-run US-equity record per Damodaran 1928-present), expense ratio (default 0.03% for VOO / VTI / SPY-class index ETFs), years to compound, federal marginal rate during contribution years (default 24%), federal marginal rate during withdrawal years (default 22%), and inflation rate (default 2.5% per the US CPI long-run average since the 1990s).

The output is a three-column side-by-side projection: Roth (tax-free terminal balance), Traditional (tax-deferred, net of the withdrawal-year tax), and Taxable brokerage (compound rate reduced by an annual tax drag derived from the contribution-year marginal rate applied to a 60/40 blended dividend-vs-LTCG mix). Each column shows the nominal terminal balance and the real (inflation-adjusted) balance in today's dollars. The methodology section below the calculator details the formulas applied.

For the underlying rules and current figures, IRS Publication 590-A (IRA contributions), Publication 590-B (IRA distributions and RMDs), Publication 560 (Retirement Plans for Small Business), and the annual IRS COLA Notice are the authoritative federal references. The SECURE 2.0 Act statutory text on IRS.gov covers the RMD age changes, super catch-up provision, and Roth 401(k) RMD elimination. The historic return assumption (~7% nominal long-run for US equities) is drawn from the NYU Stern Damodaran historical-returns database (1928-present); the inflation default is the U.S. Bureau of Labor Statistics CPI long-run average. For the UK perspective on the same compound-interest engine via the ISA wrapper, see the UK compound interest calculator, which models HMRC's ISA Manager rules instead of the IRS's IRA framework.