Why Modeling Roth Conversions and Early Retirement Withdrawals is Deceptively Hard

📌 Summary & Key Takeaways

• Spreadsheets Are Locked into 1-Year Greedy Rules: Excel and Google Sheets compute row-by-row. When you write a formula to "fill the 12% bracket," it makes a locally convenient choice for Year 1 with zero awareness of tax spikes waiting 15 years later.
• Minimizing Taxes Does Not Equal Maximizing Wealth: Paying $0 in taxes by refusing to convert Traditional balances feels great on April 15th, but it often leaves you with less spendable wealth because untaxed balances compound into massive Required Minimum Distributions (RMDs) at age 73 or 75.
• Healthcare Subsidies Dominate Ages 40 to 64: Affordable Care Act (ACA) Premium Tax Credits can be worth $10,000 to $25,000+ per year tax-free for a family. Crossing the 138% Federal Poverty Level (FPL) boundary between Medicaid and Silver Benchmark plans with Cost-Sharing Reductions is one of the steepest financial cliffs in early retirement.
• The 5-Year Rolling Lookahead Sweet Spot: A 5-year lookahead heuristic evaluates the multi-year ripple effects that 1-year rules miss—including the statutory 2-year Medicare IRMAA lag and the 5-year Roth conversion seasoning clock—evaluating candidate paths in roughly 1 to 2 seconds while enabling complete multi-decade parametric sweeps in 20 to 30 seconds on our compute server.
• Why Calculators Disagree: Different tools produce conflicting conversion advice because of varying algorithms (1-year greedy vs. 5-year lookahead), different tax law baselines, and whether they treat health insurance as an afterthought.

When I started writing simulation engines to model early retirement withdrawals, I thought the problem was straightforward. You have taxable brokerage accounts, Traditional pre-tax IRAs, and Roth IRAs. You want to pay the lowest tax rate possible while funding your annual living expenses.

It took about two weeks of coding to realize that decumulation is one of the hardest mathematical puzzles in personal finance.

During the accumulation phase, the rules are simple. Spend less than you earn, invest the surplus in low-cost index funds, and let compound growth do the heavy lifting. The sequence does not matter much.

Decumulation is completely different. It is path-dependent.

A single financial decision you make at age 45—such as converting $40,000 from a Traditional IRA to a Roth IRA—permanently alters your tax brackets, your healthcare costs, and your future Required Minimum Distributions (RMDs) decades down the road.

The Spreadsheet Trap: Why Row-by-Row Formulas Break

On popular early retirement forums, people frequently share custom spreadsheets designed to model retirement cash flows. These spreadsheets look impressive, with dozens of columns tracking balances, inflation, and federal income tax brackets.

Yet mathematically, a spreadsheet cannot optimize decumulation. It hits three structural walls.

flowchart TD
    subgraph SPREADSHEET["Spreadsheet: Linear Forward Evaluation Trap"]
        R1["<b>Age 45 (Row 1): 1-Year Greedy Formula</b><br/><code>=MIN(Trad_IRA, Top_12_Percent - Other_Income)</code><br/><i>Makes locally convenient choice for Year 1</i>"]
        R2["<b>Age 55 (Row 11): Compounding Balances</b><br/><i>Untaxed pre-tax IRA grows unabated</i>"]
        R3["<b>Age 73–75 (Row 29+): The Downstream Tax Bomb</b><br/>Mandatory RMDs force income into 24%–32% brackets<br/>Triggers top Medicare IRMAA Part B & D surcharges"]

        R1 -->|"Calculates top-to-bottom only"| R2
        R2 -->|"Zero backward visibility"| R3
    end

    style SPREADSHEET fill:#f8fafc,stroke:#cbd5e1,stroke-width:1px
    style R1 fill:#ffffff,stroke:#64748b,stroke-width:1.5px
    style R2 fill:#fef9e7,stroke:#b7950b,stroke-width:1.5px
    style R3 fill:#fee2e2,stroke:#ef4444,stroke-width:2px

1. Spreadsheets Only Calculate Forward (Top to Bottom)

In a spreadsheet, Row 2 depends on Row 1. Row 3 depends on Row 2.

When a spreadsheet user models Roth conversions, they typically hardcode a formula:

$$ \text{Conversion} = \min\left(\text{IRA Balance},\; \text{Top of 12\% Bracket} - \text{Other Income}\right) $$

In computer science, this is known as a greedy algorithm. It makes the optimal choice for the current row in isolation. It is mathematically blind to the future. It cannot look backward from age 75 to determine what you should have done at age 45.

2. The Circular Reference Nightmare

Real-world tax planning is non-linear and creates feedback loops.

Consider an early retiree at age 50:

1. Your living expenses determine how much money you must withdraw from your portfolio.
2. The account you withdraw from determines your Modified Adjusted Gross Income (MAGI).
3. Your MAGI determines your ACA Premium Tax Credit (PTC) subsidy.
4. Your subsidy determines your out-of-pocket health insurance premium.
5. Your health insurance premium changes your total living expenses for the year.

If you attempt to write formulas for this interaction in Excel or Google Sheets, the software immediately throws a #REF! circular dependency error. To resolve it, users must enable iterative calculations or write complex macros, both of which are fragile and prone to silent errors.

3. Simulation Is Not Optimization

A spreadsheet is a forward simulator, not an optimizer.

It can answer: "What happens if I manually convert $35,000 every single year until my Traditional IRA hits zero?"

It cannot answer: "Among the millions of possible withdrawal combinations across my 35-year retirement, which exact schedule maximizes my spendable after-tax wealth?"

To find that answer, you need dedicated optimization algorithms running on a compute server.

The 4 Common Ways to Model the Problem

When engineers and financial modelers build retirement engines, they generally choose from four different approaches. Each comes with distinct trade-offs.

Approach 1: The 1-Year Greedy Rule

• How it works: In each simulation year, the algorithm converts as much as possible up to a fixed bracket ceiling (such as the top of the 12% or 22% bracket).
• Where it breaks: It ignores secondary tax cliffs. A greedy rule might happily convert an extra $5,000 to "fill the 12% bracket," completely unaware that those dollars just pushed the household over an ACA subsidy cliff, costing them $8,000 in lost healthcare tax credits.

Approach 2: Exhaustive Forward Tree Search (Brute-Force Combinatorial Search)

• How it works: The algorithm starts with your actual initial portfolio balances today and branches forward through time, simulating every conceivable annual conversion amount across all 35 to 40 retirement years to find the single trajectory that maximizes terminal wealth.
• Where it breaks: Exponential branching explosion. Because retirement taxes are strictly path-dependent—requiring continuous tracking of pre-tax balances, Roth seasoning buckets, taxable cost basis, and 2-year IRMAA lookback histories—you cannot evaluate future states without first simulating forward from your starting assets. If you test just 20 conversion candidates per year across a 35-year horizon, the decision tree expands into roughly 20³⁵ (over 10⁴⁵) possible pathways. Running an unpruned brute-force search across that many trillions of possibilities is computationally impossible.

Approach 3: Multi-Year Receding Horizon Lookahead (e.g., 5-Year Window)

• How it works: For each decision year, the engine evaluates candidate actions by simulating their ripple effects across a 5-year forward window.

• Why it works: A 5-year window directly matches the two most critical multi-year tax mechanics in U.S. law:

  1. The 2-Year Medicare IRMAA Lookback: Medicare Part B and Part D surcharges at age 65 are calculated using your tax return from age 63. A 1-year model cannot see this cliff; a 5-year lookahead sees it clearly.
  2. The 5-Year Roth Conversion Seasoning Clock: Conversions made before age 59½ must sit for five tax years before principal can be withdrawn penalty-free to fund bridge spending.
  3. By scoring decisions across a 5-year rollout, the engine avoids the short-term traps of greedy models while evaluating a single lifetime trajectory in just ~1 to 2 seconds.

Approach 4: Parametric Boundary Sweeps (The AlgorithmicFIRE Approach)

• How it works: AlgorithmicFIRE synthesizes the 5-year lookahead (Approach 3) inside a two-stage optimization architecture:
  1. Boundary Pruning: Instead of testing arbitrary conversion amounts, the engine prunes the continuous income space into ~30 critical statutory boundaries per year (the standard deduction, ACA thresholds at 138%, 150%, 200%, and 400% FPL, ordinary income bracket ceilings, and IRMAA tiers).
  2. Outer Terminal Tax Rate Sweeps: To avoid assuming an arbitrary future tax rate for balances left at life expectancy, the outer loop sweeps 45+ terminal tax valuations (testing different tax penalty assumptions on remaining pre-tax vs. Roth balances).
• The engine scores each complete 35-to-40-year candidate path, identifying the globally optimal trajectory that maximizes spendable after-tax purchasing power across all accounts in roughly 20 to 30 seconds on our compute server.

Two Counter-Intuitive Truths in Decumulation Modeling

When evaluating retirement models, two major misconceptions regularly derail otherwise sound plans.

Truth 1: Minimizing Current Taxes Does Not Equal Maximizing Wealth

Many retirees focus exclusively on paying zero tax today. If they can live off taxable savings and report $0 in taxable income, they celebrate.

That is often a mistake.

If you leave a large Traditional IRA untouched during your 50s and 60s, that pre-tax balance continues to compound. By the time Required Minimum Distributions begin at age 73 or 75, that $1.5 million IRA may have grown to $3.5 million.

Suddenly, mandatory annual distributions force you into the 24% or 32% tax brackets, trigger maximum Medicare IRMAA surcharges, and make 85% of your Social Security benefits taxable.

flowchart TD
    A["<b>Traditional Pre-Tax IRA Balances ($1.5M at Age 50)</b>"]

    A -->|"Path A: Pay $0 Tax Early (No Conversions)"| P1["<b>Compounded IRA ($3.5M+ at Age 75)</b><br/>• Mandatory RMDs spike ordinary income<br/>• Pushed into 24%–32% tax brackets<br/>• Max Medicare Part B & D IRMAA surcharges<br/>• ❌ Substantially less spendable wealth"]

    A -->|"Path B: Strategic Roth Arbitrage (10%–12% Brackets)"| P2["<b>Balanced Portfolio Structure</b><br/>• Converted funds compound tax-free in Roth<br/>• Flattened pre-tax RMD liability<br/>• Protected from Medicare IRMAA surcharges<br/>• ✔️ Maximum lifetime spendable wealth"]

    style A fill:#1e293b,stroke:#0f172a,color:#ffffff,stroke-width:2px
    style P1 fill:#fee2e2,stroke:#ef4444,stroke-width:1.5px
    style P2 fill:#ecfdf5,stroke:#10b981,stroke-width:2px

Deliberately paying 10% or 12% in taxes during your early retirement "gap years" allows that money to move into a Roth IRA, where it compounds tax-free for the rest of your life with no RMDs. The goal of financial planning is not to minimize the check you write to the IRS this April; the goal is to maximize your total after-tax spendable wealth over your entire life.

Truth 2: The ACA / Medicaid Boundary Is the 500-Pound Gorilla

For early retirees under age 65, health insurance is often their single largest non-discretionary expense.

Under the Affordable Care Act, Premium Tax Credits cap health insurance premiums as a percentage of household income. For a couple in their late 50s, these subsidies are routinely worth $12,000 to $25,000+ per year tax-free.

However, the ACA introduces steep subsidy cliffs:

flowchart LR
    A["<b>0% – 138% FPL</b><br/>Medicaid Expansion<br/>• $0 Premium<br/>• County network restrictions"] --> B["<b>138% – 200% FPL</b><br/>Silver Benchmark CSR<br/>• 87%–94% Actuarial Value<br/>• Low deductibles (<$500)<br/>• Subsidized premiums"]
    B --> C["<b>200% – 400% FPL</b><br/>Standard ACA Subsidies<br/>• Sliding-scale premium caps<br/>• Standard Silver/Bronze plans"]
    C --> D["<b>>400% FPL</b><br/>Phased Subsidies<br/>• Full unsubsidized premiums<br/>• High deductible exposure"]

    style A fill:#f1f5f9,stroke:#64748b,stroke-width:1.5px
    style B fill:#ecfdf5,stroke:#10b981,stroke-width:2px
    style C fill:#eff6ff,stroke:#3b82f6,stroke-width:1.5px
    style D fill:#fef2f2,stroke:#ef4444,stroke-width:1.5px

• Under 138% FPL: In Medicaid expansion states, households earning below 138% of the Federal Poverty Level are routed to Medicaid. Medicaid offers comprehensive zero-premium care, but network access varies widely by county.
• Between 138% and 200% FPL: Households qualify for Silver Benchmark plans with Cost-Sharing Reductions (CSR). These plans provide low deductibles (often under $500) and heavily subsidized premiums.
• Between 200% and 400% FPL: Households receive standard sliding-scale premium tax credits that cap benchmark health insurance costs at 2.0% to 8.5% of household income, though without the enhanced cost-sharing deductible reductions found below 200% FPL.
• Above 400% FPL: Subsidies phase down based on statutory benchmark percentages, capping premiums at 8.5% of income under current rules.

If an algorithm blindly performs a $10,000 Roth conversion that pushes a family from 195% FPL to 215% FPL, it might cost the household $6,000 in lost subsidies and increased out-of-pocket medical deductibles to save $1,200 in federal income taxes. That is an effective marginal tax rate of over 60%.

Any retirement calculator that does not ask whether you prefer Medicaid vs. Silver Benchmark ACA coverage is missing the largest economic variable of early retirement.

Why Different Retirement Calculators Give Different Answers

If you input identical financial numbers into three different online retirement calculators, you will almost certainly get three different conversion schedules.

flowchart TD
    CALCS["<b>Identical Investor Inputs</b><br/>$1.15M Traditional IRA | $100k Annual Spend | CO Resident | Retire Age 60"]

    CALCS --> C1["<b>Calculator A (1-Year Greedy Heuristic)</b><br/>Converts up to 22% bracket immediately<br/><i>Result: Loss of $12k+ in annual ACA subsidies</i>"]
    CALCS --> C2["<b>Calculator B (Taxable First Rule of Thumb)</b><br/>Depletes taxable cash with $0 conversions<br/><i>Result: Massive RMD tax bomb and IRMAA surcharges at age 75</i>"]
    CALCS --> C3["<b>Calculator C (AlgorithmicFIRE 5-Year Lookahead)</b><br/>Harvests ACA subsidies pre-65, then ramps conversions post-65<br/><i>Result: Maximizes total spendable purchasing power</i>"]

    style CALCS fill:#1e293b,stroke:#0f172a,color:#ffffff,stroke-width:2px
    style C1 fill:#fee2e2,stroke:#f87171,stroke-width:1.5px
    style C2 fill:#fef9e7,stroke:#fbbf24,stroke-width:1.5px
    style C3 fill:#ecfdf5,stroke:#10b981,stroke-width:2px

Here is why:

1. Different Algorithmic Horizons: A 1-year greedy calculator will tell you to convert up to the 22% bracket immediately. A 5-year lookahead engine will tell you to keep income low for three years to harvest ACA subsidies, then ramp up conversions once you reach Medicare age.
2. Tax Code Assumptions: Tax laws evolve. Some calculators assume current brackets are permanent, while others still project older sunset schedules.
3. Withdrawal Sequencing Rules: Traditional rules of thumb recommend spending from Taxable accounts first, then Traditional IRAs, and finally Roth IRAs. Modern dynamic engines demonstrate that withdrawing across multiple accounts simultaneously—using cash to keep MAGI low while converting targeted pre-tax amounts—preserves higher real returns and purchasing power over retirement.
4. Healthcare Modeling: Many calculators treat healthcare as a static line item (e.g., "$1,000/month") rather than modeling dynamic Premium Tax Credits as a direct function of MAGI.

Key Takeaways for Your Own Plan

• ✔️ Treat Spreadsheets as Simulators, Not Optimizers: Use spreadsheets for annual budgeting and tracking static net worth, but recognize that top-to-bottom row formulas cannot navigate multi-decade non-linear tax cliffs.
• ✔️ Target Lifetime Spendable Wealth Over Zero Current Taxes: Intentionally fill the 10% and 12% brackets during early retirement gap years to prevent compounded pre-tax balances from forcing 24%+ tax rates and IRMAA surcharges at age 73 or 75.
• ✔️ Establish Your Healthcare Target First: If retiring before age 65, determine your state's exact 138% and 200% FPL thresholds before scheduling conversions to avoid triggering thousands of dollars in lost subsidies and higher medical deductibles.
• ✔️ Protect the Age 63 IRMAA Window: Because Medicare evaluates income with a 2-year lookback, conversion spikes at age 63 will directly inflate your Part B and Part D premiums at age 65.
• ✔️ Maintain 5 Years of Bridge Liquidity: Ensure you have enough taxable cash or brokerage assets to fund living expenses for five years so early Roth conversions have time to season before you need penalty-free access to principal.