Methodology

How Beagle calculates your retirement projection

All planning modes share one year-by-year accounting engine. This page explains its rules, the 2026 tax baseline, and the simplifications that matter when interpreting a plan.

Math-based tool — not financial advice

Beagle produces projections by running a year-by-year simulation using the assumptions you provide. Results are mathematical estimates, not guarantees. Investment returns are inherently unpredictable — past performance does not guarantee future results. Beagle does not provide personalized financial, tax, or legal advice. Consult a qualified financial advisor before making retirement planning decisions.

1. Accounts and scenarios

Shared finances and scenario overrides

Accounts, expense items, debts, and property are shared across scenarios. Income assumptions can be overridden within a scenario, including amount, start age, and end age. Scenario profiles and Roth conversions are independent. Changing a claiming age does not automatically recalculate a Social Security benefit; enter the corresponding benefit amount yourself.

Income timing

Income starts in the year you reach its start age and is paid through the year you reach its end age. Salary and part-time income with a blank end age stop at the scenario's retirement age, so retiring at 65 still includes a full year of that income at age 65.

Starting balances

Holding market values are used when available; otherwise the manual account balance is used. 401(k) and traditional IRA balances form the pre-tax bucket. Roth and HSA balances form the tax-free bucket. Brokerage and cash are tracked separately. A portfolio override scales starting balances, bond coupons, and maturities together.

Return assumptions

Equity returns use a starting-balance-weighted average within each tax bucket: holding override, then account override, then the profile rate. Bond tickers beginning UST, BOND, CORP, or MUNI are separated. Cash uses the blended holding yield, falling back to the profile cash rate when that yield is zero.

2. One accounting engine

Same rules in every projection

Regular projections, historical paths, Monte Carlo paths, and Roth comparisons use one annual accounting engine. Each year, income, required distributions, conversions, expenses, taxes, and withdrawals are applied first; the year's return then applies to what remains. This start-of-year withdrawal timing is the convention used by Bengen (1994) and the Trinity Study, and is more conservative than withdrawing after growth. Historical paths change annual returns and inflation; Monte Carlo changes annual returns.

Bonds and income

Bond principal stays at its modeled value until maturity and returns to its original tax bucket. Coupons in retirement accounts stay inside those accounts. Taxable Treasury interest is federally taxable and state-exempt; municipal coupons are included in cash income and excluded from modeled income tax. Coupons stop in the maturity year. Property equity is illiquid and never funds spending.

RMDs by birth year
RMD = prior year-end pre-tax balance / IRS Uniform Lifetime Table divisor

RMDs start at 75 for birth years 1960 onward and 73 for 1951-1959; older cohorts use their earlier start ages. The prior balance includes pre-tax bonds. If liquid pre-tax funds are insufficient, required distributions liquidate bonds at their modeled value and reduce their later coupons and maturities proportionally. Spouse-specific or inherited-account tables are not modeled.

3. Tax assumptions: 2026 baseline

Federal brackets and deductions

The engine uses 2026 IRS ordinary-income and long-term capital-gains thresholds, with basic standard deductions of $16,100 single, $32,200 joint, and $24,150 head of household. These nominal tables are held constant in future years; no future inflation indexing is assumed. Age-65 additions cover only the modeled person. The enhanced senior deduction phases out with income and expires after 2028 in projected calendar years. Itemized deductions and most other credits are not modeled.

Taxable income
Ordinary income = income streams + 85% of Social Security + RMD + conversion + taxable interest + voluntary pre-tax withdrawals

Taxable brokerage dividends are treated as qualified dividends at capital-gains rates, stacked above ordinary income. Unused deductions offset gains. Brokerage sales consume proportional cost basis and positive realized gains are taxed at long-term rates. Holding basis is shares times basis per share; balance-only accounts use their total cost basis. Missing basis uses your estimated unrealized gains percentage when provided, clearly flagged as an estimate; otherwise it is modeled as zero and flagged. Known holding basis takes precedence. New savings add basis; investment growth does not. This is a planning approximation, not tax-lot accounting. Short-term gains, capital-loss deductions/carryforwards, and net investment income tax are not modeled. Social Security inclusion is a flat 85% approximation, not the provisional-income calculation.

State tax and funding the tax bill

States use fixed effective-rate approximations, not current graduated state tax schedules. Treasury interest is excluded from their tax base. Tax on pre-tax withdrawals and brokerage gains is funded by additional withdrawals using an iterative calculation with a one-cent tolerance.

4. Spending and withdrawals

Fixed spending

Base expenses, enabled expense items, recurring large purchases, loan payments, and scenario expense adjustments determine the budget. Expenses inflate from today; historical paths compound each historical inflation observation. Disabled and expired expenses are excluded consistently.

4% of current portfolio
Annual spending target = 0.04 × current portfolio balance

This replaces the fixed budget and adjusts spending as the portfolio changes. It is not the conventional rule that starts at 4% of an initial portfolio and then inflation-adjusts that dollar amount. Success in this mode does not establish that your fixed lifestyle budget is affordable.

Fixed withdrawal order

Cash above the reserve floor funds a shortfall first, followed by brokerage, pre-tax, Roth, and finally reserved cash. Before age 59.5 the pre-tax/Roth order is reversed. This is a fixed sequence with estimated taxes, not an optimizer. Bonds are held to maturity for discretionary spending. Penalties and Roth qualification rules are not modeled.

5. Stress tests and success

Monte Carlo assumptions
Annual shock ~ Normal(0, equity fraction × 12% + bond fraction × 6%)

A shared random shock is added to each equity bucket return each year; returns are floored at -100%. Cash yields and bond coupons stay fixed. The default run count is 1,000. Portfolio mix comes from recognized holdings and defaults to equity when holdings are absent. This is a simplified normal model, not historical resampling or an asset-class correlation model.

Success means funding every year
Success rate = paths with no annual funding shortfall above $1 / total paths

A positive ending balance cannot hide an earlier unpaid expense. A later recovery does not erase failure. Exactly funding the final year counts as success even with a zero balance. The percentile curves describe balances, not guaranteed outcomes or a guarantee of any particular spending level.

Historical paths

Historical returns and inflation are replayed from the selected year. Once available history ends, a disclosed tail uses 7% returns and 3% inflation. Taxes still use the 2026 planning baseline. Benchmark modes replace non-cash asset returns and do not separately model bond coupons or maturities.

6. Roth strategy comparisons

Presets and applying a strategy

Six presets compare no conversions, $10K, $25K, $50K annually, and filling the 12% or 22% bracket. Presets operate through the year before the applicable RMD age. Applying a strategy atomically replaces the scenario conversion schedule and saves the actual bracket rule, recalculating its amount each year. It does not save a flattened annual average. Manual conversions can continue after RMD age; the RMD is distributed first.

Bracket fill is not lifetime optimization

Bracket room uses modeled income, gains, and deductions before additional withdrawals required to fund spending and conversion taxes. Those withdrawals can push final income above the target bracket. Conversions use liquid pre-tax funds; there is no optimization of bond sales, capital gains, or future healthcare premiums.

IRMAA and ACA warnings

IRMAA checks final modeled MAGI, including withdrawal taxes and municipal interest, against 2026 thresholds. Income at age 63 concerns premiums at age 65. Future thresholds are held constant and actual premium costs are not charged. ACA warnings use 400% of 2025 poverty guidelines for a 2026 coverage baseline ($62,600 single / $84,600 joint); non-taxable Social Security is included. Dependents are not modeled. No ACA threshold warning is calculated for Alaska, Hawaii, or married-separate filing. These warnings do not establish subsidy eligibility.

7. Spending estimates

Deterministic spending estimate

When a fixed-spending plan fails, a whole-dollar search reruns the same full engine with lower base spending. Conversions, RMDs, recurring expenses, and debt payments remain included. If even zero base spending cannot fund mandatory costs, no safe amount is reported.

Monte Carlo spending estimate

The search reuses up to 200 sampled paths and returns a tested lower bound that funds every year in at least 90% of that sample. The search range ends at five times current base spending. It is a sample estimate, not a guaranteed maximum. Itemized costs in additive mode remain extra, and results can change between runs.

Sources for the 2026 baseline

Reviewed September 2026: IRS federal tax adjustments, IRS distribution tables, enhanced senior deduction, CMS Medicare thresholds, and Marketplace poverty guidelines.

Known limitations

  • The plan has one modeled age and longevity; joint filing is not a two-person or survivor-benefit model.
  • State tax uses one flat rate per state applied to all income, including capital gains (Treasury interest is exempt). Local and payroll taxes, most credits, and itemized deductions are not modeled.
  • Social Security taxability is fixed at 85%; qualified-dividend treatment is assumed for brokerage dividends.
  • HSA balances are grouped with Roth assets, assuming tax-free use; non-medical HSA withdrawals and Roth basis/five-year rules are not modeled.
  • Early-withdrawal penalties are not charged. Before 59.5 the plan draws Roth money ahead of pre-tax money to avoid them; ages are whole years, so the normal order starts at 60.
  • Savings in working years go to the taxable brokerage account. Contributions to 401(k), IRA, or HSA accounts and employer matches are not modeled.
  • Bonds use current market value as maturity principal; no sale-price fluctuation or maturity-year coupon is modeled. Non-RMD spending and conversions cannot sell bonds before maturity.
  • A single inflation rate applies to expense categories. Medicare premiums, ACA subsidies, and spouse-specific tax benefits require manual assumptions.
  • Federal, IRMAA, and ACA thresholds are held at their stated baseline years for future projections. Actual future rules and inflation adjustments will differ.

Calculation validation

Beagle is checked in two ways: against published sources, so a wrong tax table or formula is caught even if every part of the engine agrees with itself, and for internal consistency across projection modes. 58 automated tests cover both, and a failing test blocks a release.

Last validated: September 2026, against the 2026 tax baseline.

Checked against published sources

2026 federal income tax: seven hand-worked households covering single and joint filers, age-65 deductions and their phase-out, the post-2028 expiry, and capital gains stacked on ordinary income.

Compared against: IRS Rev. Proc. 2025-32
All seven match to the cent.

Required minimum distributions: the divisor for every age from 72 to 120, the start age for each birth year, and the dollar amount of the first two distributions in a projection.

All 49 divisors and all start ages match.

Historical return data: the classic 4% rule (100% stocks, inflation-adjusted withdrawals, 30 years) replayed on the dataset Beagle uses for historical paths.

Compared against: Cooley, Hubbard, and Walz, AAII Journal (1998), the Trinity Study
94.9% success versus the published 95%. The two failures, 1929 and 1966, are the known worst starting years.

The full engine against an independent textbook simulation for every 30-year retirement starting from 1928 to 1995.

Compared against: Bengen, Journal of Financial Planning (1994)
All 68 starting years reach the same outcome.

Check one yourself

Single filer, age 67, $60,000 of ordinary income in 2026
Deductions     = $16,100 standard + $2,050 age 65+ + $6,000 senior
               = $24,150
Taxable income = $60,000 - $24,150 = $35,850
Federal tax    = 10% of $12,400 + 12% of $23,450
               = $1,240 + $2,814 = $4,054

Every number comes from IRS Rev. Proc. 2025-32. The enhanced $6,000 senior deduction applies in full because income is under $75,000. Beagle reports $4,054, and this exact case is one of the automated tests.

Checked for internal consistency

  • A failed year stays failed: a positive ending balance, later income, or bonds that mature later cannot hide a year that could not be paid for.
  • Spending that uses the last dollar counts as funded, the same way in every projection mode.
  • Regular, historical, and zero-volatility Monte Carlo projections of the same plan agree on balances, income, expenses, and taxes.
  • Withdrawals from 401(k) and IRA accounts are taxed, and the tax is itself paid from the portfolio, in every mode.
  • A Roth conversion strategy you apply keeps its year-by-year schedule and matches the comparison you chose it from.

These checks show that Beagle applies its stated rules correctly and reproduces published results. They are not an independent financial audit, and matching past data does not mean projections will match future markets. See the limitations above for what the model does not cover, and the research articles for worked examples.

Beagle is for educational planning purposes only. It does not constitute financial advice.