Geometric Brownian Motion (GBM)

Each asset class is projected independently using a simplified GBM model. The mean path is deterministic compound interest; the confidence bands scale with time:

mean(t)  = S₀ × (1 + r)^t
upper(t) = mean(t) × e^(+z × σ × √t)
lower(t) = mean(t) × e^(−z × σ × √t)

Mortgage Amortization

The mortgage is reduced month-by-month using standard amortization:

Monthly interest  = balance × (annual_rate / 12)
Principal payment = monthly_payment − monthly_interest

Net Worth = total liquid assets (cash + stocks + bonds) − remaining mortgage balance at each year.