FIRE Movement Model & 4% Rule
The FIRE (Financial Independence, Retire Early) framework targets early financial freedom, where annual withdrawals from investment capital cover living expenses without depleting it.
1. The 4% Rule & Safe Withdrawal Rate (SWR)
$$C_{\text{target}} = \frac{\text{Annual Expenses}}{\text{SWR}} = \text{Annual Expenses} \times 25$$
2. Savings Rate
$$\text{Savings Rate} = \frac{\text{Income} - \text{Expenses}}{\text{Income}} \times 100\%$$
3. Time to FIRE
Given starting capital $C_0$, annual contributions $A$ and real portfolio return $r$, the number of years $t$ to financial independence is:
$$t = \frac{\ln\left( \frac{C_{\text{target}} \cdot r + A}{C_0 \cdot r + A} \right)}{\ln(1 + r)}$$
It follows from the capital growth equation with year-end contributions: $C_0 (1 + r)^t + A \cdot \frac{(1 + r)^t - 1}{r} = C_{\text{target}}$. With $C_0 = 0$ it reduces to $t = \ln\left(1 + \frac{C_{\text{target}} \cdot r}{A}\right) / \ln(1 + r)$.