Methodology

Fixed-rate level payment (amortization)

Tier A — standard formula / federal rate orientation · engine mortgagePayment

Monthly principal & interest uses M = P·r(1+r)^n/((1+r)^n−1) with r = APR/12/100 and n = years×12. Optional extra principal is added after the scheduled payment.

Scope: P&I only for a fixed-rate amortizing loan. Does not price taxes, insurance, HOA, or MI.

Month-by-month amortization walk-forward

Tier A — standard formula / federal rate orientation · engine amortizationSchedule

Each month: interest = balance×monthly rate; principal = payment − interest; balance decreases. Shows balance after a selected month with optional extra principal.

Scope: Educational schedule demo; lender rounding and payment application order may differ.

FHA P&I + UFMIP + annual MIP/12 orientation

Tier B — agency consumer-education method · engine fhaPayment

Base loan = price×(1−down%). UFMIP = base×upfront rate (default educational 1.75% — confirm current schedule). Annual MIP/12 added to P&I. User can finance UFMIP.

Scope: Educational FHA cost orientation only. Official rates/duration: HUD FHA Handbook schedules.

Conventional PMI rate × loan / 12

Tier B — agency consumer-education method · engine pmiEstimate

Monthly PMI ≈ loan×annual PMI rate/12 when LTV>80%. Cancellation LTV targets reference Homeowners Protection Act orientation — confirm with servicer.

Scope: PMI pricing is lender/credit/LTV specific. Not FHA MIP.

PITI assembly (P&I + tax/12 + ins/12 + MI + HOA)

Tier B — agency consumer-education method · engine pitiEstimate

P&I from amortization identity; property tax and insurance entered annually and divided by 12; optional PMI/MIP and HOA added.

Scope: Escrow analysis may collect cushions beyond annual÷12.

Front-end / back-end ratio affordability sketch

Tier B — agency consumer-education method · engine mortgageAfford

Housing budget = min(income×front%, income×back% − other debts). Invert amortization to estimate max principal from P&I budget.

Scope: Rules of thumb for education — not a pre-approval or ATR determination.

Debt-to-income ratio (back-end / front-end)

Tier B — agency consumer-education method · engine dtiRatio

Back-end DTI = total monthly debt payments ÷ gross monthly income. Front-end = housing ÷ income. Compares to user target (often 36–43% educational band).

Scope: What counts as debt/income varies by lender and product.

Auto loan amortization with tax/fees in amount financed

Tier A — standard formula / federal rate orientation · engine autoLoan

Amount financed ≈ price + sales tax + fees − down − trade. Payment via standard amortization over term months.

Scope: Dealer products and negative equity change outcomes.

Installment loan with optional origination fee

Tier A — standard formula / federal rate orientation · engine personalLoan

Optional fee may be financed into principal. Payment via fixed-rate amortization; shows cash received vs payment principal.

Scope: Compare APR on Truth-in-Lending disclosures.

Amortizing payoff months from payment & APR

Tier B — agency consumer-education method · engine studentLoanPayoff

Months to zero balance under fixed payment using standard compound interest payoff formula. Optional IDR-style % of income is illustrative only.

Scope: Federal IDR, consolidation, and forgiveness rules are plan-specific — StudentAid.gov is authoritative.

Monthly savings vs closing costs break-even

Tier C — standard arithmetic / TVM identity · engine refinanceBreakEven

Compare old vs new P&I; break-even months = closing costs ÷ monthly savings.

Scope: Ignores tax effects, points structure, and longer-term interest totals unless you compare total interest separately.

Extra principal payoff acceleration

Tier A — standard formula / federal rate orientation · engine extraPayment

Simulates months-to-payoff with scheduled payment plus extra principal and optional lump sum.

Scope: Servicer must apply extra to principal as directed.

Compound growth + monthly contributions

Tier A — standard formula / federal rate orientation · engine compoundInterest

Monthly model grows balance by monthly rate then adds contribution. Also reports classic A=P(1+r/n)^(nt) for lump-only path.

Scope: Returns are assumptions — not guarantees. Fees/taxes reduce results.

PMT for future value goal

Tier A — standard formula / federal rate orientation · engine savingsGoal

Solves required monthly savings to reach a target given current savings and assumed yield (annuity identity).

Scope: Yield assumptions can fail; short goals prefer quoted cash yields.

CD future value from APY

Tier C — standard arithmetic / TVM identity · engine cdSimple

FV = P(1+APY/n)^(n·t) with user term and compound frequency. Optional tax haircut and early-penalty sketch.

Scope: Bank disclosures control APY and penalties. Deposit insurance limits apply.

Months-of-expenses runway heuristic

Tier D — planning heuristic · engine emergencyFund

Target cash = essential monthly spend × target months (adjusted for income volatility/dependents). Gap ÷ monthly save = months to goal.

Scope: Planning heuristic — not a regulatory standard.

Tip = base × tip% ; split grand total

Tier C — standard arithmetic / TVM identity · engine tipSplit

Tip on subtotal or tax-inclusive total; optional rounding; divide grand total by party size.

Scope: Customs and auto-gratuity policies vary.

Sales tax add/extract with user rate

Tier C — standard arithmetic / TVM identity · engine salesTax

Tax = taxable×rate; or extract pre-tax from total via total/(1+rate). Supports discounts and exempt toggle.

Scope: Not a live jurisdiction tax engine — user supplies rate.

Percent of, percent change, part/whole

Tier C — standard arithmetic / TVM identity · engine percentTool

Standard percent identities: P% of Y; (X−Y)/|Y|; X/Y×100.

Scope: Arithmetic utility.

Unit price comparison price÷size

Tier C — standard arithmetic / TVM identity · engine unitPrice

Unit price = package price ÷ size; compares two packages and cost for a needed quantity.

Scope: Assumes identical units and product quality.

Hourly ↔ annual using hours×weeks

Tier C — standard arithmetic / TVM identity · engine hourlySalary

Annual ≈ hourly×hours/week×weeks/year; inverse for hourly from salary; gross per paycheck = annual/pay frequency.

Scope: Gross conversion — not net pay. FLSA status may matter for OT.

FLSA-style OT multiplier math

Tier B — agency consumer-education method · engine overtimePay

Regular + OT hours×rate×multiplier + optional double-time hours×2×rate.

Scope: Exemptions and state daily OT rules may apply.

Employee FICA: SS up to wage base + Medicare (+ Additional Medicare)

Tier A — standard formula / federal rate orientation · engine ficaWithhold

SS = min(gross, remaining wage base room)×SS rate; Medicare = gross×Medicare rate; Additional Medicare on wages over threshold orientation.

Scope: Educational — payroll systems and IRS Pub 15 / SSA base control live withholding.

Rough net pay from effective tax % + FICA + deductions

Tier B — agency consumer-education method · engine takeHomeRough

Applies user effective federal/state rates to a pre-tax-adjusted monthly gross, plus FICA rates, plus benefits deductions.

Scope: Not Form 1040 and not the IRS Withholding Estimator.

Effective tax rate = tax ÷ base

Tier C — standard arithmetic / TVM identity · engine effectiveTax

Effective rate on taxable income and all-in rate including optional FICA vs gross; contrasts with marginal bracket input.

Scope: Filing status, credits, and AMT can change true rates.

Revolving balance payoff under APR & payment

Tier B — agency consumer-education method · engine creditCardPayoff

Month loop: apply monthly interest then payment; or minimum = max(floor, % of balance). Counts months and interest.

Scope: Issuer minimum formulas vary by agreement.

Snowball vs avalanche multi-debt simulation

Tier D — planning heuristic · engine debtPayoffPlan

Orders debts by APR (avalanche) or balance (snowball); applies illustrative minimums then throws remaining budget at target debt.

Scope: Simplified counseling-style math — not a credit plan.

Assessed base × rate − exemptions

Tier C — standard arithmetic / TVM identity · engine propertyTax

Taxable assessed = value×assessment ratio − exemptions; annual tax = base×rate%; monthly = annual/12.

Scope: Local millage definitions differ (mills vs percent).

Cash-to-close sketch: down + net closing costs

Tier B — agency consumer-education method · engine closingCost

Closing ≈ price×% + points + prepaids − credits; cash to close ≈ down + net closing.

Scope: Replace with Loan Estimate / Closing Disclosure.

Rent cash outlay vs ownership cash & equity sketch

Tier D — planning heuristic · engine rentVsBuy

Compares cumulative rent to ownership cash flows and rough equity (appreciation − remaining balance) over a horizon.

Scope: Heuristic — ignores many frictions and taxes.

Gallons = miles/MPG; cost = gallons×price

Tier C — standard arithmetic / TVM identity · engine fuelCost

Classic trip fuel cost; optional EV kWh/100mi comparison.

Scope: Real economy varies with conditions.

Price from markup or margin; margin = profit/price

Tier C — standard arithmetic / TVM identity · engine markupMargin

Markup% on cost vs gross margin% of price; solves unit price and multi-unit profit.

Scope: Does not include overhead allocation.

Break-even units = (fixed + target profit) / contribution margin

Tier C — standard arithmetic / TVM identity · engine breakEven

Contribution = price − variable cost; units to cover fixed costs and optional profit target.

Scope: Single-product CVP model.

Invoice subtotal − discount + tax + shipping − deposit

Tier C — standard arithmetic / TVM identity · engine invoiceTotal

Sums line items, applies discount and tax percentages, adds shipping, subtracts deposit.

Scope: Tax collection rules are jurisdiction-specific.

Self-employed tax set-aside sketch (SE + income tax)

Tier B — agency consumer-education method · engine contractorSetAside

Net = revenue − expenses; SE tax on ~92.35% of net × combined SE rate; income tax on proxy taxable after optional QBI haircut; quarterly = tax/4.

Scope: Not Schedule C / SE. Wage base and §199A limits apply — use IRS estimated tax tools or a CPA.

I = P·r·t

Tier A — standard formula / federal rate orientation · engine simpleInterest

Simple interest with year or day-count basis (360/365).

Scope: Most consumer amortizing loans are not simple-interest only.

Years to double ≈ 72 / rate%; exact via logs

Tier C — standard arithmetic / TVM identity · engine ruleOf72

Rule-of-72 approximation plus exact years = ln(multiple)/ln(1+r) and sample FV path.

Scope: Approximation quality varies by rate.

Future cost = amount×(1+i)^t

Tier B — agency consumer-education method · engine inflationPower

Purchasing-power projection with constant inflation; optional income raise path and real growth.

Scope: Actual CPI path from BLS differs from constant assumptions.

26 half-payments ≈ 13 monthly equivalents

Tier C — standard arithmetic / TVM identity · engine biweeklyMortgage

Biweekly payment often monthly/2; annual cash ≈ 13 monthly payments accelerating payoff vs 12.

Scope: Servicer program rules and fees vary.

Down = price×%; cash goal = down + closing buffer

Tier C — standard arithmetic / TVM identity · engine downPayment

Computes target down payment, optional closing %, gap vs savings, months at save rate.

Scope: Gift/assistance documentation rules apply.

Side-by-side amortization total cost

Tier A — standard formula / federal rate orientation · engine loanComparison

Builds payment and total of payments for two offers including financed fees; flags lower total cost.

Scope: Still compare official APR disclosures.