This page is ground truth you can check yourself. Every case below was computed by hand from the cited primary source — IRS Rev. Proc. 2025-32, IRS Notice 2025-67, IRS Publications 915 and 590-B, the CMS 2026 Medicare premium release, the SSA 2026 fact sheet, and the HHS poverty guidelines — with every intermediate step shown, and then compared against the engine. The hand numbers were not derived from the engine's own tables; a mismatch in either direction is a finding. Each case is also a permanent automated test, so the engine is re-checked against this exact arithmetic on every release. All cases use official tax year 2026 values, no inflation indexing, and $0 state tax unless stated.
Two of these cases (V1 and V2) were additionally hand-verified by an independent external reviewer during the August 2026 100-scenario validation review — both reconciled to the dollar.
For every case in this table, the engine's output equals the hand-computed value exactly (to the cent).
| Case | Inputs | Hand computation | Result | Source |
|---|---|---|---|---|
| V1 — Ordinary tax (external anchor) | Single, wages $100,000, standard deduction, under 65 | Deduction $16,100 → taxable $83,900. 10% × 12,400 = 1,240 12% × 38,000 = 4,560 22% × 33,500 = 7,370 | Federal $13,170, marginal 22% | Rev. Proc. 2025-32 |
| V2 — Ordinary tax (external anchor) | Single, wages $200,000 | Taxable $183,900. 1,240 + 4,560 + 22% × 55,300 = 12,166 + 24% × 78,200 = 18,768 | Federal $36,734, marginal 24% | Rev. Proc. 2025-32 |
| V3 — FICA | Wages $200k and $300k, single; $200k MFJ | $200k: 6.2% × 184,500 wage base = 11,439 + 1.45% × 200,000 = 2,900. $300k adds 0.9% × (300,000 − 200,000) = 900 above the additional-Medicare threshold. $200k MFJ: 250k threshold not reached — same as single. | $14,339 / $16,689 / $14,339 | SSA 2026 fact sheet |
| V4 — Ordinary tax, MFJ | MFJ, $200,000 pre-tax withdrawals, age 60 | Deduction $32,200 → taxable $167,800. 10% × 24,800 = 2,480 12% × 76,000 = 9,120 22% × 67,000 = 14,740 | Federal $26,340, marginal 22% | Rev. Proc. 2025-32 |
| V5 — Social Security taxability | Single, SS $40,000, other income $30,000 | Provisional income = 30,000 + ½ × 40,000 = 50,000. Tier 1 = min(20,000, ½ × (34,000 − 25,000)) = 4,500. Taxable = min(85% × 40,000, 4,500 + 85% × (50,000 − 34,000)) = min(34,000, 18,100) | Taxable SS $18,100 | IRS Pub 915 (thresholds frozen in law) |
| V6 — Capital-gains stacking | Single, $60,000 ordinary + $50,000 long-term gains, age 60 | Taxable $93,900; gains stack above the $43,900 ordinary layer. Ordinary: 1,240 + 12% × 31,500 = 5,020. Gains: $5,550 fills the 0% bracket to $49,450; $44,450 at 15% = 6,667.50. | Federal $11,687.50 (gains portion $6,667.50) | IRS QDCGT worksheet; Rev. Proc. 2025-32 |
| V7 — 0% gains bracket | Single, $20,000 ordinary + $25,000 gains, age 60 | Taxable $28,900 — gains end below the $49,450 zero-rate cap, so the gains tax is $0. Ordinary layer $3,900 × 10%. | Federal $390, gains tax $0 | Rev. Proc. 2025-32 |
| V8 — Medicare IRMAA | MFJ MAGI $250,000 (both on Medicare); single MAGI $520,000 | MFJ first tier (above $218,000): ($81.20 Part B + $14.50 Part D) × 12 × 2 persons = 2,296.80. Single top tier (above $500,000): ($487.00 + $91.00) × 12 = 6,936.00. Exactly $218,000 is not above the threshold → $0. Part B amounts are CMS’s published (dime-rounded) figures, corrected Aug 2026 from formula-derived values. | $2,296.80 / $6,936.00 / $0 | CMS 2026 premium release |
| V9 — ACA premium tax credit | Household of 2, MAGI $60,000, benchmark silver $18,000/yr | FPL(2) = 15,650 + 5,500 = 21,150 (2025 guidelines — the prior year's, as the law prescribes). 60,000 ÷ 21,150 = 283.7% FPL → interpolating the 250–300% row (8.44% → 9.96%) gives 9.4641%. Credit = 18,000 − 9.4641% × 60,000. | Credit $12,321.53; above 400% FPL the credit is $0 (cliff) | Rev. Proc. 2025-25; HHS 2025 guidelines |
| V10 — RMDs | $1,000,000 prior-year balance | Age 75 divisor 24.6 → 40,650.41; age 73 divisor 26.5 → 37,735.85; before the start age → $0. Start age: born 1959 → 73; born 1960 or later → 75. | $40,650.41 / $37,735.85 / $0 | IRS Pub 590-B; SECURE 2.0 |
| V11 — QCD | Single, age 74, $80,000 withdrawal ($50,000 of it RMD), $30,000 QCD, year 2026 | QCD used = min(30,000 requested, 50,000 RMD, $111,000 2026 limit) = 30,000 — excluded from income. Ordinary $50,000; deduction 16,100 + 2,050 (65+) + 6,000 (senior bonus, AGI under $75k) = 24,150 → taxable 25,850. Tax = 1,240 + 12% × 13,450. | Federal $2,854 | IRC §408(d)(8); Rev. Proc. 2025-32 |
| V12 — Senior bonus phase-out | Single, age 70, $100,000 ordinary, year 2026 | Phase-out = 6% × (100,000 − 75,000) = 1,500 → bonus 6,000 − 1,500 = 4,500. Deduction 16,100 + 2,050 + 4,500 = 22,650 → taxable 77,350. Tax = 1,240 + 4,560 + 22% × 26,950. | Federal $11,729 | OBBBA (2025–2028); Rev. Proc. 2025-32 |
| V13 — Standard deduction variants | Age 70 single and MFJ; years 2026 and 2029 | Single 2026: 16,100 + 2,050 + 6,000 = 24,150. MFJ 2026 (both 65+): 32,200 + 2 × 1,650 + 2 × 6,000 = 47,500. Single 2029 (bonus expired): 18,150. Under 65: 16,100. | $24,150 / $47,500 / $18,150 / $16,100 | Rev. Proc. 2025-32; OBBBA expiry |
| V14 — Net investment income tax | Single, $150,000 ordinary + $100,000 gains | AGI $250,000. NIIT = 3.8% × min(100,000 investment income, 250,000 − 200,000 threshold) = 1,900. Ordinary layer tax 24,734 + gains at 15% = 15,000 + 1,900. | Federal $41,634 (NIIT $1,900) | IRC §1411 (threshold frozen in law) |
| V15 — Early-withdrawal penalties | Age 50: $40,000 early pre-tax + $10,000 HSA non-medical + $5,000 taxable 529 earnings | 10% × 40,000 + 20% × 10,000 + 10% × 5,000 = 4,000 + 2,000 + 500. | Penalties $6,500 | IRC §72(t), §223(f), §529(c) |
| V16 — Child tax credit | MFJ, wages $450,000, 2 qualifying children | Gross credit 2 × 2,200 = 4,400; phase-out 5% × (450,000 − 400,000) = 2,500 → credit 1,900. Taxable 417,800 → tax before credit 86,608. | Federal $84,708 (credit $1,900) | IRC §24 as amended by OBBBA; Rev. Proc. 2025-32 |
| V17 — ACA credit, Form 8962 arithmetic | Household of 2, MAGI at exactly 200% FPL ($42,300), benchmark $15,000 | Applicable figure at 200% = 6.60% (Rev. Proc. 2025-25). Contribution = 42,300 × 6.60% = 2,791.80. Credit = 15,000 − 2,791.80. | Credit $12,208.20 | Form 8962 method; Rev. Proc. 2025-25 |
| V18 — ACA credit, family of four | Household of 4 (FPL $32,150), MAGI at exactly 300% ($96,450), benchmark $20,000 | Applicable figure at 300% = 9.96%. Contribution = 9,606.42. Credit = 20,000 − 9,606.42. | Credit $10,393.58 | Form 8962 method; HHS 2025 guidelines |
| V19 — Quick Start SS estimate vs the SSA formula | Incomes at each bend point, mid-scale, and the cap | SSA bend-point formula (2026 parameters from the constants table): 90% to $1,286 AIME, 32% to $7,749, 15% above, capped at $4,152/mo. AIME $1,286 → $13,888.80/yr; AIME $7,749 → $38,706.72; $60k income → $28,150.56; above the $184,500 wage base → capped $49,824. Rounded to the nearest $500. | $14,000 / $38,500 / $28,000 / $50,000 (estimate-only input — never used in tax math) | SSA PIA formula |
Beyond the cases above, the automated suite tests every important 2026 threshold at $1 below, exactly at, and $1 above: each ordinary-bracket edge for all four filing statuses (with the cumulative hand arithmetic written next to each constant), the capital-gains 0% and 15% caps, the Social Security taxability thresholds and the 85% ceiling, every Medicare IRMAA tier, the NIIT threshold, the ACA 400%-FPL cliff and the low-income floor, the FICA wage base and additional-Medicare thresholds, the OBBBA senior-bonus phase-out points, and RMD divisor spot checks at 80/90/100. Every expected value is hand-derived from the governing release, never from the engine's tables.
Single-year checks prove the tax math; this schedule proves the multi-year plumbing — withdrawal gross-up, deduction changes over time, and depletion — on a plan simple enough to verify with a pencil. A single retiree, 65 in 2026, holds $500,000 in one pre-tax account and spends $50,000 a year, with 0% investment return, 0% inflation, no Social Security, no state tax, and no other inputs. Each year the withdrawal W must cover spending plus the tax on W itself:
| Year | Age | Deduction | Withdrawal | Federal tax | Ending balance |
|---|---|---|---|---|---|
| 2026 | 65 | $24,150 | $53,243.18 | $3,243.18 | $446,756.82 |
| 2027 | 66 | $24,150 | $53,243.18 | $3,243.18 | $393,513.64 |
| 2028 | 67 | $24,150 | $53,243.18 | $3,243.18 | $340,270.45 |
| 2029 | 68 | $18,150 | $54,061.36 | $4,061.36 | $286,209.09 |
| 2030 | 69 | $18,150 | $54,061.36 | $4,061.36 | $232,147.73 |
| 2031 | 70 | $18,150 | $54,061.36 | $4,061.36 | $178,086.36 |
| 2032 | 71 | $18,150 | $54,061.36 | $4,061.36 | $124,025.00 |
| 2033 | 72 | $18,150 | $54,061.36 | $4,061.36 | $69,963.64 |
| 2034 | 73 | $18,150 | $54,061.36 | $4,061.36 | $15,902.27 |
| 2035 | 74 | $18,150 | $15,902.27 (all that remains — below the deduction, so tax is $0) | $0 | $0 — shortfall ≈ $34,098 |
| 2036+ | 75+ | — | $0 | $0 | $0 — shortfall $50,000/yr |
The engine reproduces this ledger with each year's withdrawal and tax within $1 of the closed form. The balance identity — ending balance = prior balance − withdrawal at 0% return — holds to the cent in every year, and the automated tests assert all of it: the two withdrawal levels, the deduction step, the balance identity, the $0-tax partial year at 74, and the exact depletion shape.
This library validates the engine's calculations against hand arithmetic from primary sources — it is not a claim that projections predict the future, and it does not cover every modeled rule (the methodology page lists the full rule-by-rule validation table, the IRS-worksheet cross-checks, and everything deliberately excluded). State tables remain Tax Foundation 2025 data with uniform inflation indexing, the remaining disclosed limitation, scheduled for the January 2027 review. The library grows with each annual table review.
Free educational tool — not tax, legal, or investment advice. See the Disclaimer. Found an arithmetic error on this page? That is a finding — please report it: [email protected].