Retirement planning models the multi-decade balance between compounding investment growth, career savings duration, and living expense inflation.

### Mathematical Framework The calculator evaluates retirement readiness across four sequential equations: 1. **Future Monthly Expenses:** Projected living expenses compound at annual inflation over working years: $\text{Future Expense} = \text{Current Expense} \times (1 + r_{\text{inf}})^t$. 2. **Target Nest Egg (4% Rule):** Required corpus equals 25 times future annual expenses: $\text{Corpus Needed} = \text{Future Annual Expense} \times 25$. 3. **Accumulated Portfolio Value:** The sum of future value of current savings and future value of recurring monthly contributions compounded at expected return $r$: $$FV = PV \times (1 + r/12)^n + m \times \frac{(1 + r/12)^n - 1}{r/12}$$ 4. **Funding Progress:** Percentage of target corpus funded: $(\text{Accumulated Portfolio} / \text{Corpus Needed}) \times 100%$.

### Worked Numeric Example A 30-year-old planning to retire at age 60 (30-year accumulation horizon) currently spends $3,000 monthly, holds $25,000 in starting savings, contributes $500 per month, and projects an 8.0% annual investment return alongside 4.0% annual inflation: 1. In 30 years at 4.0% inflation, monthly living expenses compound from $3,000 to $9,730.20, requiring an annual retirement budget of $116,762.40. 2. Applying the 25x safe withdrawal multiplier establishes a **Target Corpus of $2,919,060**. 3. Compounding the $25,000 starting savings yields $273,391, while contributing $500 monthly adds $745,180, producing an **Accumulated Portfolio of $1,018,571**. 4. The projected nest egg leaves a **savings gap of -$1,900,489** (the portfolio is 35% funded), demonstrating that increasing monthly contributions or extending retirement age is required to close the shortfall.