Calculation Methodology & Sources

Model version 1 , October 27, 2026

All money is in today's USD. Spending and savings maintain their purchasing power as prices change. Investment return and inflation are effective annual rates, not nominal APRs. The model applies a constant return and no withdrawals before retirement.

1. Size the retirement target

F = monthly retirement spending × 12 ÷ (initial withdrawal rate / 100)

This is target sizing. It is not a withdrawal simulation or a probability of success. A smaller selected withdrawal percentage gives a larger target for the same budget.

2. Remove inflation exactly

G = (1 + nominal return / 100) ÷ (1 + inflation / 100)

real annual rate = G − 1

monthly real rate m = G^(1/12) − 1

The default 7% return and 3% inflation imply a real rate of approximately 3.8835%. These inputs are illustrative assumptions, not observations of future growth. When inflation exceeds return, G is below one and purchasing power falls.

3. Find the Coast number today

K = F ÷ G^(retirement age − current age)

K is the balance that would reach F with no further deposits under the selected growth assumptions. The current gap is max(0, K − current savings).

4. Locate a possible Coast month

Let P be current savings, C monthly savings and n elapsed months. For end-of-month deposits:

B(n) = P × (1+m)^n + C × A(n)

A(n) = ((1+m)^n − 1) ÷ m, or n when m is zero.

K(n) = F ÷ G^(years remaining after n months)

The first month satisfying B(n) ≥ K(n) gives the Coast age. The engine uses a numerically stable annuity expression and only a negligible floating-point comparison tolerance. If no crossing occurs by retirement, it reports that rather than inventing a later date.

The green chart line continues saving through retirement for comparison. It does not stop deposits automatically at the first Coast crossing. The second line stops deposits today. Both lines and the threshold use today's purchasing power.

5. Solve for the required savings pace

For N total months:

required monthly savings = max(0, (F − P × G^years) ÷ A(N))

additional monthly savings = max(0, required monthly savings − entered monthly savings)

The annual additional amount is twelve times the monthly result. This calculation does not assess income or affordability.

Bounds, zero values and rounding

Ages must be whole numbers, current age 18-99 and target age 19-100, strictly after current age. A target above 90 carries a planning-horizon caution. Money inputs allow zero and reject negative or nonfinite values. Returns from −20% to 25%, inflation 0%-15% and initial withdrawal rates 0.5%-15% are accepted as exploration bounds, not recommendations. Empty inputs suppress results.

Zero spending creates a zero target and an explicit explanation. Equal return and inflation produce zero real growth without division by zero. Crossing ages round up to the first month. Displayed dollars round to whole dollars; CSV balances use cents. Calculations retain unrounded values.

Assumptions and omissions

Monthly savings stay constant in real dollars, so nominal deposits would rise with inflation. Investments are left untouched before the target date. Taxes, fees, asset allocation, benefit payments, contribution limits, early-access penalties, market sequences, health shocks and post-retirement withdrawals are not calculated. No success probability is produced.

Sources and scope

The 4% input is a user-editable sizing example. William Bengen's original 1994 research, reprinted by FPA in 2004 is historical context, not a guarantee. Bengen's own updated explanation describes later research and why historical findings should not become a personal prescription. Our model does not reproduce those historical portfolio simulations.

The tool does not use a claimed historical stock-market average or CPI series: 7% and 3% are scenarios. The BLS CPI program is a reference for understanding inflation, not a feed to this calculator. Current CPI values were not imported.

For a separate account or benefit analysis, consult the IRS 2026 retirement-account limits and SSA retirement age information. Those rules are not implemented here and require year-specific verification before being used in another tool.

Review and corrections

Created by Retire Growth. No financial certification or independent professional review is claimed. Tests verify worked examples, zero-rate behavior, negative real growth, invalid inputs and share-parameter handling. They do not establish suitability for a personal plan. Contact support@retiregrowth.com for corrections. Return to the calculator.