सं
SanchitaFIRE
Back to Calculator

Mathematical Methodology

Complete Computational Blueprint, Recurrence Formulas & Audit Trail

1. Phase 1: Wealth Accumulation (Growing Annuity)

Unlike basic compound interest calculators that assume flat monthly savings, Sanchita models salary raises and merit increases via discrete annual Step-Up geometric hikes:

C(m) = C(m - 1) × (1 + r_m) + SIP(m)
SIP(m) = SIP_0 × (1 + s)^floor((m - 1) / 12)

Where r_m = (1 + r_pre)^(1/12) - 1 represents the exact monthly effective interest rate.

2. Phase 2: Retirement Decumulation & Drawdown

Post-retirement, the portfolio generates monthly investment returns while funding living expenses that compound annually with inflation:

C(m) = C(m - 1) × (1 + r_post_m) - E(m)
E(m) = E_retirement × (1 + inflation)^floor((m - 1) / 12)

3. Safe Withdrawal Rate (SWR) Calculation

The initial safe withdrawal rate is defined rigorously as the first year's annual retirement living cost divided by the peak accumulated retirement corpus:

SWR = (Monthly Living Expense at Retirement × 12) / Peak Corpus

4. Open-Source Verification Package

All underlying mathematical formulas are independently verified and open-sourced in our public GitHub library at abirbandy/sanchita-fire-math.

Sanchita — Reflective Financial Memoir & Independence EngineOpen FIRE Simulator →