What every retirement projection assumes
The depletion and sustainable-withdrawal tools use one constant monthly return and one withdrawal per month, without extra deposits. The employer and investment tools described below also support contributions. Fees and taxes are not separately charged; enter a return and withdrawal amount that reflect whatever treatment you choose to assume. USD is a display unit, and all calculations use unrounded values.
Inputs accept balances and monthly withdrawals from zero to one trillion dollars, annual return and inflation assumptions from −99% to 100%, and a withdrawal duration of 1 to 100 whole years in the interface. These are software input limits, not claims about plausible outcomes.
Annual rates and inflation
Annual inputs are effective compound rates. We do not divide an annual percentage by twelve. With inflation adjustment enabled, the exact real annual growth factor is (1 + nominal return) ÷ (1 + inflation). The corresponding monthly return is:
Rates in these equations are decimal fractions. With inflation off, the inflation input is ignored and r is nominal. With inflation on, a constant withdrawal in real dollars corresponds to a nominal withdrawal that increases each month with inflation. The stated monthly amount is valued at time zero; an end-of-month first payment incorporates the first month’s inflation. All balance values then show time-zero purchasing power.
How long a balance lasts
For an end-of-month payment W from balance B, the balance recurrence is B(next) = B(current) × (1 + r) − W. After n payments, its algebraic balance is B × (1 + r)^n − W × [(1 + r)^n − 1] ÷ r. Setting this to zero gives:
At r = 0, n = B ÷ W. For beginning-of-month payments, the recurrence is [B(current) − W] × (1 + r), and the depletion equation replaces W with W × (1 + r). The first beginning-of-month payment occurs immediately at month zero; the first end-of-month payment is at month one.
The equation yields a potentially fractional number of payment periods. The calculator reports the number of full payments and the scheduled calendar month of the last payment. For example, 2.5 end-of-month payments means two full withdrawals and a smaller final withdrawal at month three. Exact integer results have no additional partial withdrawal.
With a positive return, an end-of-month withdrawal no larger than B × r is covered indefinitely in this constant model. The beginning-of-month threshold is B × r ÷ (1 + r). A positive balance and zero withdrawal also never reaches zero mathematically, including when the modeled return is negative. A zero starting balance is reported as empty immediately.
Green: end-of-month payments, final payment at month 12. Blue: beginning-of-month payments, final payment at month 11.
$12,000 starting balance
Start → 12 months, $0 remaining
Example: $1,000 monthly, zero return and inflation.
Sustainable monthly withdrawal
For n = 12 × years, rearranging the same cash-flow equation gives the payment that ends at zero:
At zero return, W = B ÷ n. For beginning-of-month payments, divide the end-of-month amount by (1 + r). “Sustainable” describes this model only; it is not a probability-of-success statement or a safe-withdrawal recommendation.
Chart and rounding conventions
The chart starts with the initial balance and plots balances after each scheduled payment. Beginning-of-month scenarios include the immediate withdrawal at month zero. Withdrawals stop when the balance is exhausted. The depletion and sustainable-withdrawal chart is limited to 50 years; if funds remain, the caption explicitly says so. The table provides annual snapshots and the last displayed point.
Display amounts are rounded to whole dollars. Calculations keep full numerical precision; near-integer payment counts and negligible residual balances are normalized to avoid showing an extra payment caused solely by floating-point arithmetic. Logarithms and exponentials use numerically stable log1p and expm1 forms near zero returns. The tool rejects a withdrawal horizon when an extreme combination of positive return and duration makes its final-balance correction indistinguishable from a perpetual payment in floating-point precision. Tiny positive balances are not treated as depleted merely because they round to zero dollars.
The 4% illustration
The mini calculator multiplies the entered portfolio by 0.04 and divides that first-year amount by twelve for a monthly equivalent. This page illustrates a starting percentage followed by inflation-adjusted dollar withdrawals, not taking 4% of the changing balance every year. It does not simulate historical portfolios.
Roth conversion tax and break-even comparison
The 2026 data file contains the ordinary-income brackets for single, joint, head-of-household, and separate filers from IRS Revenue Procedure 2025-32, section 4.01. The tool calculates progressive tax on ordinary taxable income before and after adding a fully taxable distribution, then subtracts the first figure from the second. Income must already be after deductions.
Let C be the distribution amount, T the incremental tax, f the entered future tax rate, g the retirement account growth factor, and h the after-tax outside-money growth factor at the chosen year. Both retirement accounts use the same assumed investment return.
Convert with withheld tax: Roth value = (C − T) × g
Keep traditional: after-tax value = C × g × (1 − f)
Outside opportunity cost = T × h
Net comparison = Roth value − traditional after-tax value − outside opportunity cost
Outside opportunity cost is zero for the withheld-tax option. The break-even future rate is (T ÷ C) × (h ÷ g) with outside tax payment and T ÷ C with withholding. For outside tax payment and different growth rates, the crossing year is ln[(T ÷ C) ÷ f] ÷ ln[(1 + account return) ÷ (1 + outside return)], if the result is finite and nonnegative. A zero conversion has no meaningful break-even rate.
The Roth model assumes the future Roth withdrawal has no additional tax. It does not determine qualified distribution status. It excludes after-tax basis, state taxes, penalties, capital gains interactions, credit or deduction changes, surtaxes, benefit and premium effects, and required distributions. “Keep traditional” is a single future-tax endpoint, not a complete annual withdrawal plan.
Employer-plan and investment cash flows
The 403(b), 457(b) and TSP tools divide each annual employee and employer contribution by twelve and deposit that amount at every month-end. Annual dollar inputs remain fixed over the whole projection; the 2026 age setting affects only a separate standard contribution reference.
The investment tool allows fixed nominal monthly deposits and fixed or inflation-indexed withdrawal requests. Cash flows occur at the selected beginning or end of month. Deposits precede withdrawals. If available money cannot meet a request, only the available balance is paid; the model records a shortfall, creates no debt and continues future scheduled deposits.
Nominal balance divided by accumulated inflation gives purchasing power in starting dollars. Investment gain equals ending balance minus starting balance minus deposits plus withdrawals actually paid. The graph and yearly table cover the selected one-to-100-year horizon. The first exhaustion month can precede the first unfunded payment when a payment exactly empties the account.
| Starting balance | $12,000 |
|---|---|
| Deposits: $300 × 12 | +$3,600 |
| Paid withdrawals: $100 × 12 | −$1,200 |
| Investment gain | $0 |
| Ending balance | $14,400 |
2026 contribution references
IRS Notice 2025-67, pages 1–2, supplies the 2026 base, ordinary age-50 and replacement ages-60–63 limits. Figures are stored with their source in the dated data file. The 457(b) reference includes employee and employer deposits; non-governmental 457(b) plans receive no age-based catch-up.
The standard panel does not determine compensation limits, other-plan coordination, special 403(b) service catch-ups, the special 457(b) pre-retirement provision, Roth catch-up eligibility, TSP service-specific benefits, or vesting. An above-reference assumption is flagged but still projected; being below the reference is not personal contribution approval. Page-specific IRS sources and conditions appear on the 403(b), 457(b) and TSP pages. Reviewed October 25, 2026.
Sources and review date
- IRS Revenue Procedure 2025-32, section 4.01 (PDF): tax year 2026 bracket thresholds, reviewed October 25, 2026.
- IRS Roth IRAs overview: official account guidance referenced October 25, 2026. Eligibility rules are outside this calculator.
- Fidelity, “How can I make my savings last?”, May 26, 2026: starting withdrawal percentage and inflation-adjustment convention, reviewed October 25, 2026. No historical success rates from that article are used here.
The cash-flow formulas and worked examples above are mathematical derivations rather than external forecasts. For a reproducible example, open the depletion calculator and enter $120,000, $1,000 monthly, zero return, and inflation off: the balance funds 120 payments.