How every calculator works under the hood

Core formulas

All calculators on this site use the same shared math library (assets/calc.js). Single source of truth for these standard finance formulas:

Monthly payment for an amortizing loan (PMT)

For principal P, monthly rate r, and total payments n:

PMT = P × (r × (1 + r)^n) / ((1 + r)^n − 1)

Used for: every mortgage, refi, auto loan, home equity loan calculation. This is the standard amortizing-loan formula.

Remaining loan balance after k payments

Balance(k) = P × (1 + r)^k − PMT × ((1 + r)^k − 1) / r

Used for: figuring out what you'd still owe at any given month — needed for hold-period comparisons (ARM vs fixed) and total-cost analyses.

Future value of a series of payments (annuity)

FV = PMT × ((1 + r)^n − 1) / r

Used for: the pay-off-vs-invest comparison. Projecting what regular investments would grow to over a horizon.

Months to payoff if you increase the payment

months = ln(PMT / (PMT − P × r)) / ln(1 + r)

Used for: bi-weekly mortgage and extra-principal-payment calculations. Requires the payment to be high enough to cover monthly interest, otherwise loan never pays off.

Break-even point

Break-even months = upfront cost / monthly savings

Used for: every refinance scenario, deductible-optimizer, and similar "is this worth the up-front pain" comparison.

Per-calculator assumptions

01 — Insurance deductible optimizer

• Annual premium savings = (old premium − new premium). User-supplied.
• Expected-value calculation: annual savings minus probability-of-claim × extra deductible cost.
• Claim-frequency options: 0%/yr (never), 10%/yr (once in 10), 20%/yr (twice in 10), 33%/yr (3+ in 10). Historical pattern is the best predictor.
• Typical premium-savings ranges (referenced on the calc page): $500→$1,000 deductible = 5-10% premium drop; $1,000→$2,500 = 8-15%; $1,000→$5,000 = 20-30%. Source: NAIC rate-factor industry publications.
• State carveouts: CA, HI, MD, MA, MI restrict how credit-based insurance scores may be used in pricing. The calculator does not model these state-specific rules.
• Verdict thresholds: ✅ if break-even < 4 yrs AND claim freq ≤ 10% AND can cover from savings. ⚠️ if 4-8 yrs OR moderate claim history. ❌ if > 8 yrs OR can't cover.

02 — ARM vs fixed mortgage

• ARM "worst case" = lifetime cap rate applied after the fixed period ends, re-amortized over remaining months.
• Total cost over hold = (ARM monthly × months at start rate) + (worst-case monthly × months after adjustment) for stays past the fixed period.
• Net wealth = total paid + remaining balance at exit.
• "Average homeowner stays ~13 years" anchor (used in the hold-period default + 12-month-buffer rationale): National Association of Realtors Profile of Home Buyers and Sellers, multi-year average.
• Verdict thresholds: ✅ if hold ≤ fixed period − 12 months buffer. ⚠️ if hold right at fixed period. ❌ if hold > fixed period AND worst-case payment unaffordable.

03 — Pay off mortgage early vs invest

• Effective mortgage rate: nominal × (1 − marginal tax rate) if itemizing, else nominal rate.
• After-tax investment return: full return for tax-advantaged (Roth) accounts; return × 0.85 for taxable (assumes 15% LTCG, the most common bracket for filers with taxable income up to ~$500k MFJ); return × (1 − marginal × 0.85) for traditional accounts (drag at withdrawal).
• Wealth at horizon: pay-down path = FV of freed-up cashflow after mortgage paid off + interest saved. Invest path = FV of equivalent monthly contribution.
• Investment-return defaults (used in the calc's hint text + verdict logic): S&P 500 long-term ~10% nominal / ~7% real (inflation-adjusted). For an honest comparison against a nominal mortgage rate, we recommend 7-8%. Source: Robert Shiller S&P 500 historical data, widely-cited.
• Verdict thresholds: Tie if within 5%. ✅ Invest if > 15% advantage. ⚠️ Invest if 5-15%. ✅ Pay down if > 10% advantage to paydown. ⚠️ Pay down if 5-10%.

04 — Bi-weekly mortgage

• Bi-weekly equivalent monthly payment = monthly × 13/12 (26 half-payments per year = 13 full payments).
• Total fees over loan life = setup fee + (per-payment fee × biweekly payment count).
• Verdict thresholds: ✅ if fees = $0. ❌ if fees ≥ interest saved. ❌ if fees > 20% of interest saved. ⚠️ if fees modest but DIY captures same.

05 — 30-to-15 refinance

• New monthly = PMT(balance + costs, new rate, 180 months) if costs rolled in.
• Front-end ratio = new monthly ÷ gross monthly income. Industry standard: lender max 28%.
• Back-end DTI = (new monthly + other debt) ÷ gross monthly income. Industry standard: lender max 36-43%.
• Verdict thresholds: ❌ if front-end > 32% (affordability risk). ❌ if back-end > 43%. ⚠️ if rate spread < 0.25% (refi math weak). ✅ if front-end ≤ 25% AND interest saved > $30k.

06 — PMI removal refinance

• Current monthly outlay = P&I + PMI. New monthly = P&I only (assumes 20% equity to avoid new PMI).
• PMI typical range (referenced on the calc page): $50-$400/month for the average homeowner. Source: industry-published rate factors; varies by LTV, credit score, and loan size.
• Break-even = closing costs ÷ (current outlay − new P&I).
• Lifetime interest delta includes 5 years of PMI you would have otherwise paid (conservative estimate of years before automatic termination under HPA 1998).
• Verdict thresholds: ❌ if savings ≤ 0. ⚠️ if conventional and rate alone doesn't save (try free cancellation first). ✅ if break-even < 24 months and rate also drops. ✅ if break-even < 36 months. ⚠️ 36-60 months. ❌ > 60 months.

07 — HELOC vs cash-out refi

• HELOC total cost = (HELOC rate × amount × years) + setup fees, amortized.
• HELOC stress test = rate + 1.5% (typical rate-rise scenario over a multi-year payback).
• Cash-out refi cost includes the hidden cost of re-rating the existing first mortgage at today's rate.
• Verdict thresholds: ✅ HELOC if current rate < cash-out rate − 1% AND payback ≤ 7 years. ✅ Cash-out if current rate > cash-out rate + 0.5% AND payback ≥ 10 years. ⚠️ if margin < 10%.

08 — Home equity loan vs cash-out

• HEL total cost = (HEL rate × amount × years amortized) + closing costs.
• Cash-out refi cost includes total interest on new full loan + closing costs − interest you'd have paid on existing first mortgage anyway.
• Verdict thresholds: ✅ HEL if current rate < refi rate − 1%. ✅ Cash-out if current rate > refi rate + 0.5%. ⚠️ Close call if within 10%.

09 — FHA to conventional

• Equity check: LTV = balance ÷ home value. If > 80%, new conventional loan would still have PMI (defeats purpose).
• Current outlay = P&I + FHA MIP. New outlay = conventional P&I (assumes ≤ 80% LTV).
• FHA annual MIP default (used in the calc's hint text + verdict logic): 0.55% of loan balance for most modern FHA loans. Source: HUD Mortgagee Letter 2023-05 (Feb 2023) which reduced annual MIP by 30bp.
• Conventional PMI assumption if > 80% LTV: 0.5% annually for sensitivity.
• Lifetime MIP eliminated = current MIP × 12 × years remaining on original loan.
• Verdict thresholds: ❌ if LTV > 80%. ❌ if savings ≤ 0. ✅ if break-even < 24 months. ✅ if < 36 months. ⚠️ if 36-60 months.

10 — Lease vs buy

• Buy total = loan total + maintenance after warranty ($1,500/yr) − vehicle value at horizon.
• Lease total = (downcost + monthly × term + disposition fee + excess mileage cost) × number of cycles in horizon.
• Excess mileage charge: $0.20/mile (industry typical).
• Disposition fee: $400/cycle (industry typical).
• Verdict thresholds: ⚠️ if horizon < 5 years (comparison unfair). ✅ Buy if margin > 25% over horizon. ✅ Buy if any positive margin and horizon ≥ 5 years.

11 — Auto loan refi

• LTV = balance ÷ vehicle value. Underwater flag if > 100%.
• Total savings = (current total payments) − (new total payments + fees).
• Term-extension trap: flagged if new term > current term by > 12 months AND total savings negative.
• FICO rate-shopping window: 14 days. Multiple auto-loan rate inquiries within this window count as a single hard inquiry for FICO scoring. Shop aggressively within the window, not across months.
• Vehicle-age cutoff: cars older than 10 years are often hard to refinance regardless of credit — lender approval typically requires ≤ 10 years, ≤ 100k-125k miles. Source: industry-published lender guidelines (LendingTree, RateGenius, credit unions).
• Verdict thresholds: ❌ if underwater. ❌ if term extended AND total cost higher. ✅ if rate drop ≥ 2% AND term not extended AND savings > $1,000.

12 — Mortgage refi break-even (general)

• Cash costs = closing costs if paid out of pocket, $0 if rolled in.
• If lender-paid: assumes rate rises 0.25% to compensate.
• Break-even = cash costs ÷ monthly savings (P&I delta).
• Net effect over stay = monthly savings × stay months − cash costs.
• Verdict thresholds: ❌ if savings ≤ 0. ✅ strong if < 12 months break-even, no term reset. ✅ if 12-36 months. ⚠️ if 36-60 months. ❌ if stay < break-even.

What the calculators don't model

• Tax-loss harvesting in the invest-vs-paydown comparison. Real after-tax returns on taxable accounts are often a bit better than the flat 0.85 multiplier we use.
• State income tax. Federal marginal only. State tax adds another 0-13% drag depending on where you live.
• AMT, NIIT, phase-outs. Edge cases for high earners.
• Refinancing costs paid via points (specifically). The "no-cost" toggle approximates this but doesn't model points precisely.
• Insurance state-specific rules. CA, HI, MD, MA, MI restrict credit-based pricing — the deductible optimizer doesn't model these.
• Lender-specific quirks. Some lenders cap the rate buydown, won't refi certain LTV bands, or require seasoning. We assume vanilla terms.

Updating cadence

Calculators are reviewed and updated:

• Quarterly for rate environment assumptions (when 30-year fixed rates change meaningfully).
• Annually for tax law changes (TCJA sunsets, IRMAA brackets, etc.).
• Immediately if a calculation error is identified.

Last methodology review: 2026-05-12. If you spot something wrong, file a correction at the contact address on the about page.