How Our Calculators Work

Standard Repayment

Uses the same amortization formula as mortgages, with a 10-year (120 payment) term.

Income-Driven Repayment (IDR)

Payment = 10% of discretionary income (or 5% for some newer plans)

Discretionary income = AGI - (150% × Federal Poverty Level for family size)

Note: We use estimated poverty level figures. Actual calculations may vary.

Future Value with Contributions

FV = PV(1 + r)ⁿ + PMT × [((1 + r)ⁿ - 1) / r]

• FV = Future value at retirement
• PV = Present value (current savings)
• r = Annual return rate
• n = Years until retirement
• PMT = Annual contribution

The 4% Rule (Safe Withdrawal Rate)

Annual Income = Portfolio Value × 0.04

Based on the Trinity Study, withdrawing 4% of your portfolio annually (adjusted for inflation) has historically provided a high probability of lasting 30 years. This is a starting point, not a guarantee.

Employer Match Calculation

Match = min(Your Contribution, Salary × Match Limit) × Match Rate

Example: If employer matches 50% up to 6% of salary, and you earn $100,000 contributing 6%, your match = $6,000 × 50% = $3,000/year.

Tax Savings (Traditional 401k)

Annual Tax Savings = Contribution × Marginal Tax Rate

Contributions reduce your taxable income in the year you make them.

FIRE Number (Target Portfolio)

FIRE Number = Annual Expenses × 25

Based on the 4% rule: if you need $40,000/year, you need $1,000,000 invested. The multiplier of 25 is the inverse of 4%.

Years to FIRE

Years = ln((FI Number × r + Annual Savings) / (Current × r + Annual Savings)) / ln(1 + r)

This accounts for compound growth of existing savings plus regular contributions. Higher savings rates dramatically reduce time to financial independence.

Debt Avalanche (Mathematically Optimal)

Order: Pay minimums on all debts, then apply extra payments to the highest interest rate debt first.

Result: Minimizes total interest paid over the life of all debts.

Debt Snowball (Psychological Wins)

Order: Pay minimums on all debts, then apply extra payments to the smallest balance first.

Result: Quicker wins as small debts are eliminated, potentially higher total interest.

Monthly Interest Calculation

Monthly Interest = Balance × (APR / 12)

Each month, interest accrues on the remaining balance before your payment is applied.

Marginal vs Effective Tax Rate

Marginal Rate: The tax rate on your last dollar of income (your tax bracket).

Effective Rate: Total tax ÷ Total income (your actual average rate).

Effective Rate = Total Tax Owed / Taxable Income

Progressive Tax Calculation

Income is taxed in layers. For 2024 single filers: first $11,600 at 10%, next $35,550 at 12%, next $53,375 at 22%, and so on. Only income within each bracket is taxed at that rate.

Note: We use current IRS tax brackets. State taxes are not included.

Capital Gain Calculation

Capital Gain = Sale Price - Cost Basis

Cost basis includes purchase price plus any fees or commissions paid.

Short-Term vs Long-Term

Short-Term (held < 1 year): Taxed as ordinary income at your marginal rate.

Long-Term (held ≥ 1 year): Taxed at preferential rates: 0%, 15%, or 20% depending on income.

Simple ROI

ROI = (Final Value - Initial Investment) / Initial Investment × 100%

Shows total percentage gain or loss, but doesn't account for time.

Annualized Return (CAGR)

CAGR = (Final Value / Initial Value)^1/years - 1

Compound Annual Growth Rate shows the smoothed annual return, making it easier to compare investments held for different periods.

Current Yield

Current Yield = Annual Coupon Payment / Current Price × 100%

Simple measure of income relative to price paid.

Yield to Maturity (YTM)

YTM is the total return if the bond is held until maturity, including:

• • All coupon payments
• • The difference between purchase price and face value
• • Assumes coupons are reinvested at the YTM rate

YTM is calculated using numerical approximation (no closed-form solution).

Total Cost of Buying

Includes: mortgage payments, property taxes, insurance, maintenance (typically 1% of home value/year), HOA fees, closing costs, and opportunity cost of down payment.

Total Cost of Renting

Includes: rent payments (with annual increases), renter's insurance, plus the investment growth of money that would have gone to down payment and maintenance.

Break-Even Analysis

We calculate when (if ever) buying becomes cheaper than renting, accounting for home appreciation, equity buildup, and the investment returns you'd earn by renting and investing the difference.

Primary Insurance Amount (PIA)

Based on your Average Indexed Monthly Earnings (AIME) from your highest 35 years of earnings, run through a progressive formula with "bend points" that replace more of lower earnings.

Claiming Age Adjustments

• Age 62: ~30% reduction from full retirement age (FRA)
• Full Retirement Age (66-67): 100% of PIA
• Age 70: ~24-32% increase from FRA (8%/year delayed credits)