Methodology

Every number this site shows is reproducible. This page describes the model precisely enough to reimplement it — because we did exactly that, twice, and require the two implementations to agree to the cent.

The deterministic projection

• Money is integer cents throughout; balances are quantized to whole cents after every monthly step using banker's rounding (round half to even).
• Each month, in order: contributions are added (respecting the $5,000/yr aggregate and $2,500/yr employer caps in source order — clipped amounts are reported, never silently dropped), then the balance grows by the monthly return factor and monthly fee factor, then one quantization.
• Monthly factors derive from annual inputs as (1 + annual)^(1/12), computed with deterministic software ln/exp so results are bit-identical on every device.
• "Today's dollars" figures deflate each month's nominal balance by the cumulative inflation factor.
• Contributions respect the statutory floor (July 4, 2026) and the federal seed applies only to eligible birth dates (2025–2028).

The ranges (Monte Carlo)

• Monthly geometric Brownian motion: each month each simulated path multiplies by exp(μ − σ²/2 + σZ) with μ the monthly log-return, σ the monthly volatility (annual σ / √12), and Z a standard normal draw.
• Randomness is seeded (xoshiro128** + Marsaglia polar transform): the same scenario and seed reproduce identical percentiles anywhere, which is why shared links always agree.
• We report the 10th/25th/50th/75th/90th percentiles across 5,000 paths (fewer via the public API, which reports the count it used). The shaded chart bands are the middle 50% and 80%.
• The Monte-Carlo implementation is validated against the closed-form lognormal moments in our test suite.

Verification

• An independent Python reimplementation regenerates golden test vectors; the TypeScript engine must match them exactly — to the cent for projections, bit-for-bit for Monte-Carlo percentiles.
• 300 randomized fuzz scenarios spanning ages 0–119, cap collisions, and every schedule type are cross-checked the same way on every build.
• Property-based tests enforce invariants (more contributions never yield less; with zero growth and fees, final balance equals seed + contributions exactly; percentiles are ordered).
• Exports (PDF/Excel) are tested to contain exactly the engine's numbers.

What the model does not claim

Future returns. The deterministic path uses your assumed average return; the bands show the spread implied by your volatility assumption. Real markets can fall outside any modeled range. Tax figures are simplified estimates using your assumed rate. This is education, not advice.

The full source, including the reference implementation and test suite, is public: github.com/zach-eikenberry/530A.