Horizon: 30 years. Portfolio ruin means the invested balance hits $0 within that window.
Real returns: compound annual growth is set by the slider above (default 5%, adjustable 0–10%), with 15% standard deviation (roughly a diversified stock-heavy portfolio). The CAGR figure is a real return — already net of inflation — so all dollar inputs stay in today's purchasing power.
Social Security: a constant real annuity that offsets total spending. Portfolio only funds the shortfall (total spending − SS). Set to $0 if not applicable.
Expenses: total spending = household spending (slider) + fixed expenses (Medicare, housing, taxes, maintenance). All are real dollars per year.
Method: finite-horizon reciprocal-gamma approximation. The stochastic present value of the shortfall stream is fit to a reciprocal-gamma distribution matched to its exact mean and variance under geometric Brownian motion; ruin probability is one Gamma CDF evaluation — no simulation.
Monte Carlo cross-check: simulates 25,000 30-year paths with monthly steps under the same GBM, subtracting shortfall/12 each month. The two methods should agree to within Monte Carlo noise (~±0.3% at 25k trials). Large gaps hint the closed-form's tail approximation is straining — usually at high withdrawal rates.
This is a rough teaching tool, not financial advice.