Tool · Projections
Roth IRA Growth Projector
Multi-decade tax-free compounding — with age-50 catch-up contributions, Monte Carlo percentile bands, sequence-of-returns stress tests, and an inflation-adjusted (real) view. Every formula documented below.
All calculations run locally in your browser. Your inputs are never transmitted or stored.
Profile
Contributions
The 2026 base IRA limit is $7,500 (§219(b)(5)(A), indexed; IRS Notice 2025-67).
Per §219(b)(5)(B). Catch-up starts the year you turn 50.
Rough proxy for IRS annual indexation of the limit.
Return assumptions
Historical US equity σ ≈ 15–18%. 60/40 portfolio ≈ 10–12%.
Last run: paths · seed
Inflation & display
Real = nominal balance ÷ (1 + inflation)yr. Shows purchasing power in today's dollars.
Sequence-of-returns stress
Same average return — but what if the worst 10 years land at the beginning, the end, or the middle of your horizon? During accumulation, sequence matters less than in withdrawal — but it still shapes confidence intervals.
The stressed decade earns this annualized return; the remaining years compensate to keep the full-horizon geometric mean equal to your expected return.
End balance
Real:
Nominal:
Total contributed
Including catch-up
Tax-free growth
% on basis
Balance trajectory
Median path + 10/90th bands ( runs)
Percentile outcomes at end of horizon
Across simulated paths with return ~ N(%, %). All balances are .
10th
25th
Median
75th
90th
When you cross key balances
Deterministic path · $
Sequence-of-returns stress test
All three scenarios end at the same geometric mean return. Only the order changes. During pure accumulation (no withdrawals), differences are modest — but the gap widens dramatically the moment you start drawing down.
Year-by-year projection
Deterministic path · $. Rows shaded where you first cross a milestone.
| Age | Year | Contribution | Annual growth | Balance | Real | Nominal |
|---|---|---|---|---|---|---|
+ marks years where the catch-up contribution applies.
User Guide
How to use the Roth IRA Growth Projection tool
This tool projects your Roth IRA balance over time under three scenarios: a deterministic projection at a chosen return assumption, a Monte Carlo simulation showing the range of likely outcomes, and a stress-test scenario modeling sequence-of-returns risk near withdrawal age. The output is a terminal balance distribution, a year-by-year median path, and the probability of reaching various target balances.
Simple compound-growth calculators give you a single number — "at 7% for 30 years, $7,500/year grows to X." That number is almost certainly wrong in practice, because markets don't deliver the same return every year. Sequence-of-returns variation means two investors with identical 30-year average returns can end up with terminal balances that differ by a factor of two or more. This tool captures that reality.
Who should use this tool
Anyone building a retirement plan who wants to know the range of likely outcomes, not just the point estimate. Particularly useful for pre-retirees within ten years of first withdrawal, because that's the window where sequence risk matters most — a bad five-year stretch right before or after retirement can permanently reduce your sustainable withdrawal rate.
Young contributors asking "is $7,500 a year enough?" also benefit: the Monte Carlo shows you the percentile outcomes, so you can see the tenth-percentile (bad) path as well as the fiftieth (typical).
Walking through the inputs
Starting balance. Current Roth IRA total. Include Roth 401(k) if you'll roll it over at retirement.
Annual contribution. The dollars you'll add each year. The tool assumes constant real contributions; if you plan to increase with inflation, enter the real (inflation-adjusted) amount.
Years to projection horizon. Time from today until the terminal balance you care about — typically retirement date or end of the contribution window.
Asset allocation. Equity percentage drives the return and volatility assumptions. Default is 70/30 for under-age-50 and 60/40 for age-50-plus. The tool uses historical US equity and bond return distributions.
Monte Carlo iterations. The number of paths to simulate. Default 10,000 is plenty for stable percentile estimates.
How to read the result
The main chart shows the median balance year by year, with shaded bands for the tenth-to-ninetieth percentile range. The terminal distribution shows the balance at the horizon at each percentile. A "probability of reaching $X" gauge lets you check specific targets.
The sequence-of-returns stress test isolates the impact of poor early years: it runs the same return distribution but forces the first three years to be in the bottom decile. The resulting terminal balance is usually 10–25% lower than the baseline median — that's the "sequence penalty" you'd want to protect against in real life.
Common mistakes this tool prevents
- Assuming deterministic returns. A projection that says "you'll have $1.2M" should really say "the median is $1.2M, but there's a 20% chance you're below $800K and a 20% chance you're above $1.7M." The distribution matters more than the point estimate.
- Ignoring volatility drag. Geometric return is always less than arithmetic return when volatility is positive. The tool uses geometric compounding.
- Forgetting fees. A 1% annual expense ratio compounds to roughly a 20% haircut over 30 years. Enter your actual blended expense ratio.
- Using nominal instead of real returns. If you're planning for real-world purchasing power at retirement, work in real returns throughout. Inflation is roughly 2–3% real, so a 7% nominal return is a 4–5% real return.
- Extrapolating unusually strong recent years. The 2020–2021 returns were far above long-run averages. Don't anchor your expected return to the last few years.
After you have the projection
Compare the median terminal balance to your retirement income target using a reasonable safe withdrawal rate (typically 3.5–4% real). If the tenth-percentile outcome doesn't meet your floor, either increase contributions, extend the horizon, or lower the withdrawal-rate assumption. If the ninetieth-percentile looks excessive, that's good — you have upside flexibility.
For multi-account planning (Traditional plus Roth plus taxable), use the Asset Location Architect to optimize placement across wrappers.
Worked example: $50K balance, $7.5K/year contributions, 30-year horizon
Maya, age 35, has $50,000 in her Roth IRA and contributes $7,500 each year. She holds a 70 % US stocks / 30 % bonds allocation through a low-cost index portfolio (0.05 % blended expense ratio). Her planning horizon is age 65, 30 years out. She wants to know: what's a realistic range of outcomes?
The deterministic projection at 5 % real return gives $724,000 at age 65 (in today's dollars). That's the headline number most calculators report.
The Monte Carlo adds the distribution around that point estimate. Using historical US 70/30 return volatility (about 12 % annualized), the tool's 10,000-iteration simulation returns: 10th percentile $430,000, 25th $560,000, median (50th) $720,000, 75th $910,000, 90th $1.18M. The median is close to the deterministic projection — reassuring — but the 10th-to-90th range spans nearly 3x. Maya's retirement plan should work under the 10th-percentile outcome (probably by contributing more, working longer, or lowering withdrawal rate), not just the median.
The sequence-of-returns stress test — forcing the first three years into bottom-decile outcomes — produces a terminal median of $595,000, about 18 % below the baseline median. This quantifies the "bad luck early" risk. Because Maya is 30 years from withdrawal, she has time to recover; the stress-test result matters more to someone within 10 years of retirement. She notes it but doesn't change her plan.
Maya uses the "probability of reaching $600K" gauge, which returns 66 %. That's her estimated probability of having $600K in today's dollars at 65 under her current contribution plan. If she wants 80 % confidence, she needs to raise contributions modestly (the tool shows $9,000 per year gets her there) or extend her horizon to 67. She chooses to increase contributions when her income rises — the tool flagged that her plan is sound but conservative.
The chart that best captures this for her is the shaded "fan" showing percentile bands over time — she can see the range widen as compounding accumulates uncertainty, and she can see the median path tracking the deterministic projection. It's a much more honest picture than any single-number answer.
Methodology
How the projector computes every number
These accordions expose every formula, assumption, and IRS citation. Numbers you see above are produced entirely from the disclosed equations — nothing is hidden.
1. Base compounding identity
The deterministic path uses annuity-due accumulation — contributions are credited at the start of each year and earn the full year's return:
By+1 = (By + Cy) × (1 + r)With B0 = starting balance, Cy = contribution in year y (indexed for catch-up and inflation as configured), and r = your expected annual return. After n years this is equivalent to the closed-form:
when contributions are constant. When contributions change year to year (e.g. when catch-up kicks in at age 50), we compute iteratively.
2. Age-50 catch-up contribution
Under §219(b)(5)(B), taxpayers aged 50 or older by the end of the taxable year may contribute an additional $1,100 (2026) to a traditional or Roth IRA on top of the base limit.
The IRA age-50 catch-up was indexed for the first time under SECURE 2.0 §108 for 2026 (IRS Notice 2025-67) — rising from the long-standing $1,000 to $1,100. The tool applies $1,100 flat for the 2026 input year.
If you toggle "escalate contribution by inflation," only the base limit tracks inflation — the $1,100 catch-up remains constant in this model, consistent with current law.
3. Monte Carlo — lognormal returns
Annual returns are drawn from a lognormal distribution calibrated so that the arithmetic mean equals your expected return m and the arithmetic standard deviation equals your volatility s. The calibration is:
Each year's return is then R = exp(μlog + σlog·Z) − 1, where Z ~ N(0,1) is sampled via the Box-Muller transform from two independent uniforms. Paths compound independently:
Percentiles (10/25/50/75/90) are computed at each year across all paths, then plotted as bands on the chart. Increasing the number of runs tightens the band estimates; 1,000+ runs is a reasonable default.
Limitations: lognormal i.i.d. returns assume no autocorrelation, no mean reversion, and no fat tails. Real-world returns exhibit all three. This is a tool, not a crystal ball — use the percentile spread as a proxy for uncertainty, not a forecast.
4. Sequence-of-returns stress test
The "bear decade at start" and "bear decade at end" scenarios hold the geometric mean return constant — they only rearrange the order in which returns arrive.
(1+rbear)10 × (1+rrest)n−10 = (1+rexpected)nWe solve for rrest so the full-horizon geometric mean matches your assumption. During pure accumulation, the two orderings typically produce close end balances — often within 10–20%. During decumulation the order matters far more, which is why sequence-of-returns is the central risk of early retirement.
The early-bear scenario can actually outperform the baseline for accumulators who keep contributing through the downturn — new contributions buy at depressed prices and ride the recovery up. This is the technical basis for dollar-cost averaging and the argument against trying to time bear markets when you're still accumulating.
5. Real vs. nominal
Every balance is computed first in nominal dollars (the literal dollars in the account). The real-dollar view divides by cumulative inflation:
Balancereal, y = Balancenominal, y / (1 + i)yReal dollars are what your portfolio can buy in today's terms. Over 30 years at 2.5% inflation, $1 nominal becomes about $0.48 real. It's the number that actually matters for planning.
When you toggle inflation-escalated contributions on, Cy increases by (1+i)y — modeling the assumption that IRS indexation keeps the base limit moving with CPI. This roughly holds: the IRA limit has moved from $2,000 (1982–2001) through $6,000 (2019–22) to $7,000 (2024–25) and $7,500 (2026), a compound rate close to CPI over the long run.
6. What this tool does not model
Clear-eyed disclosure of limitations:
- Taxes on non-qualified distributions. All balances assume distributions, if taken, are qualified (post-59½ and 5-year clock satisfied). See Withdrawal Explainer for ordering rules.
- Income phase-outs. Contributions assume you're under the §408A(c)(3) MAGI phase-out. High earners may need the backdoor route.
- Early-withdrawal penalties. Distributions before 59½ of earnings trigger a 10% §72(t) penalty unless an exception applies.
- Fees. Expense ratios and advisory fees are not subtracted. Reduce your expected return input by your all-in fee to bake them in.
- Returns autocorrelation / fat tails. Lognormal i.i.d. is a simplification. Actual markets have momentum, mean reversion, and occasional tail events that don't fit the distribution.
- Required distributions. Roth IRAs have no lifetime RMDs under §408A(c)(5). Inherited Roth IRAs do, under the 2024 final regs — covered separately.
7. Sources & citations
All rules cited here link to primary sources in the site archive:
- Contribution limits — 2026 base limit ($7,500), catch-up ($1,100), MAGI phase-outs.
- Core Roth IRA rules — §408A summary.
- Asset placement — what belongs in a Roth to maximize tax-free compounding.
- Withdrawal Explainer — qualified-distribution rules and ordering.
- IRC §219(b)(5) — contribution limits and catch-up mechanics.
- IRC §408A — Roth IRA statutory framework.
- SECURE 2.0 Act §109 — catch-up indexation for employer plans (not IRAs).
Educational content only — not tax, legal, or investment advice. Every number above is produced by open, disclosed formulas.