Retirement Income Analysis

Determine how long your savings will last during retirement under different payout models.

Status: Algorithmic Audit (CPA Review Pending)
Jurisdiction: United States (IRS & SSA Standards)
Tax Year / Constants: 2026 Statutory Limits
Data Privacy: 100% Client-Side In-Browser

The Mathematical Formula

Years Sustained (t) = -ln(1 - (Balance × r) / Annual Drawdown) / ln(1 + r)

Variable & Parameter Definitions

  • Years Sustained (t) Total years the retirement portfolio will last before balance reaches zero.
  • Balance Total retirement portfolio capital on retirement day one.
  • r Annual portfolio investment return rate during retirement.
  • Annual Drawdown Total dollar withdrawals taken out each year for living expenses.

Real-World Worked Scenario: Testing a $1,000,000 Portfolio with $65,000 Annual Withdrawals

A retiree with a $1,000,000 portfolio withdraws $65,000 annually (a 6.5% initial withdrawal rate) with a 5.0% annual portfolio return.

  1. Annual Net Cash Drain: $65,000 withdrawal exceeds $50,000 annual interest (5% of $1M), draining principal by $15,000 in Year 1.
  2. Numerator Calculation: -ln(1 - (1,000,000 × 0.05) / 65,000) = -ln(1 - 0.7692) = -ln(0.2308) = 1.4663.
  3. Denominator Calculation: ln(1 + 0.05) = ln(1.05) = 0.04879.
  4. Portfolio Longevity: 1.4663 ÷ 0.04879 = 30.05 Years.
  5. Outcome: The portfolio exhausts completely in Year 30. Lowering withdrawals to $50,000/year (5% SWR) extends portfolio longevity indefinitely.
Key Financial Takeaway: Exceeding the safe withdrawal rate accelerates portfolio exhaustion exponentially because principal depletion compounds rapidly.

Strategic Insights & Pitfalls to Avoid

  • ✓ The Perpetual Yield Threshold: When Annual Drawdown ≤ Balance × r, the portfolio mathematically never depletes.
  • ✓ Required Minimum Distributions (RMDs): Factor in mandatory IRS RMD withdrawals starting at age 73.
  • ✓ Bucket Strategy: Keep 2 to 3 years of living expenses in liquid cash/CDs, 5 years in fixed income, and remainder in equities to ride out bear markets.

Frequently Asked Questions

Why is withdrawing 6% or 7% risky in retirement?

If a 20% to 30% market downturn occurs early, high withdrawal rates force you to sell shares at rock-bottom prices, permanently impairing recovery potential.

What happens if annual withdrawals are less than annual interest?

Your principal balance grows over time, creating a legacy estate for heirs or charities.

How does inflation impact portfolio longevity?

If you increase withdrawals annually for inflation while returns remain flat, the portfolio exhausts faster than fixed-nominal models suggest.

Related Decision Calculators

Retirement Planner Create a comprehensive retirement savings plan based on current a... Required Minimum Distribution (RMD) Calculate your IRS required minimum distributions (RMD) based on ... Social Security Distribution Calculate how taxes impact your Social Security benefit distribut... Annuity Calculator Determine annuity payout amounts, fixed term payments, or lifetim...