Calculator methodology

The amortization formula

The base monthly payment for a fixed-rate, fully-amortizing loan is:

M = P · r(1 + r)n / ((1 + r)n − 1)

• M = monthly payment (principal + interest)
• P = principal balance
• r = monthly interest rate (APR ÷ 12)
• n = total number of monthly payments (term in months)

This is the standard Truth-in-Lending Act formula; it's what every U.S. bank, credit union, and online lender uses to build the amortization schedule on a fixed-rate loan. The same formula powers the homepage calculator, every loan-type calculator, and the refinance break-even math.

How interest accrues month by month

We compute one month at a time. Each month:

1. Interest charge = balance × (APR ÷ 12)
2. Principal portion = monthly_payment − interest_charge
3. New balance = balance − principal_portion
4. Apply any extra payment or lump sum directly to balance (see next section)

This is why the same monthly payment is mostly interest at the start and mostly principal at the end — interest scales with the remaining balance, which shrinks every month. The early-payment asymmetry that makes prepayment so effective comes directly from this loop.

How extra payments are applied

Extras (recurring monthly extra OR a one-time lump sum) are applied directly to principal in the same month they post. That means the next month's interest charge is calculated on the already-reduced balance.

Practical implication you should know about: most U.S. servicers default to applying borrower-initiated extra payments toward future scheduled payments, not toward current principal — that's the "principal-only" vs "paying ahead" distinction. Our calculator assumes principal-only application because that's the correct way to see the math. On the operational side, you usually have to instruct your servicer in writing to apply extras to principal; otherwise your headline payoff date moves but interest savings don't materialize the way the calculator shows.

Multi-debt cascade (avalanche / snowball)

The multi-debt strategy comparator runs three parallel simulations on the same input list:

• Avalanche: debts ordered by APR (highest first). Every dollar of extra goes to the top-ordered active debt.
• Snowball: debts ordered by remaining balance (smallest first). Same extra-allocation rule.
• Equal split: the extra is divided pro rata across all active debts. The reference baseline.

The cascade is the part most calculators get wrong. When a debt finishes, its minimum payment doesn't disappear — it cascades into the extra-payment pool for the remaining debts. That's why an avalanche or snowball plan accelerates over time rather than running on a fixed extra. We model this explicitly: once a debt's remaining balance hits zero, its minimum payment is added to the running extra pool from the next month forward.

Each scenario terminates when all debts hit zero (or after 600 months — the safety cap). Output: total interest paid and months to debt-free, side-by-side.

Where default values come from

Every calculator opens with seeded defaults that reflect a typical mid-market borrower. The defaults are chosen to be realistic, not extreme — so your first paint is close to a real loan, and the math output isn't cartoonishly large or small.

• Auto loan defaults ($30k @ 7.5%, 60mo) — Experian State of Auto Finance Q4 2025; Federal Reserve G.19 Consumer Credit (auto-loan rate trends).
• Student loan defaults ($40k @ 6.5%, 120mo) — Education Data Initiative federal undergraduate averages; Department of Education annual data.
• Mortgage defaults ($400k @ 7%, 360mo) — Freddie Mac Primary Mortgage Market Survey (PMMS).
• SBA 7(a) defaults ($250k @ Prime + 2.75%, 120mo) — SBA.gov FY2025 lending averages; Wall Street Journal Prime Rate.
• Small business loan defaults ($100k @ 11%, 60mo) — typical bank/online lender mid-market terms.
• HELOC defaults — variable-rate Prime + margin; Wall Street Journal Prime Rate as the index reference.
• VA / FHA / USDA — funding-fee, MIP, and annual- fee parameters from official program rules at va.gov, hud.gov, and rd.usda.gov.

All defaults are intentionally seeded to a realistic mid-market scenario, not the cheapest-possible or worst-possible. Override them with your own loan numbers — the math doesn't care, and the default is just a starting point for comparison.

Sourcing for narrative claims (rate trends, regulatory changes, FOMC commentary) follows the rules in editorial policy.

What the calculators don't model

Honest limitations matter more than feature lists in YMYL math. Here's what the calculators above explicitly don't compute, so you can adjust mentally when your situation hits one of these:

• Precomputed-interest loans (Rule of 78s).Common on subprime auto loans. The interest is locked in at origination, so paying off early doesn't save the back-loaded interest the calculator implies. Read your loan document; if it says precomputed or Rule of 78s, call the servicer for an actual payoff quote before sending a lump sum.
• Factor-rate loans (MCAs). Some merchant cash advances and factor-rate online business loans charge a flat multiple (e.g., 1.30) regardless of payoff timing. Prepayment saves zero on those products. Our amortizing calculators do not apply.
• Variable-rate resets. ARMs, HELOCs, and some SBA loans reset on a Prime-based index. The calculator assumes a fixed APR. For variable products, run scenarios with the projected reset rate to see actual exposure.
• Tax effects. Mortgage-interest deduction (where it applies) and student-loan interest deduction reduce your effective rate; business-loan interest is generally deductible. Our calculators show pre-tax interest. Multiply the savings by (1 − marginal tax rate) for an after-tax view.
• PMI / MIP / annual fees.Mortgage insurance and USDA/FHA fees are real cost components that don't live in the amortization formula. The relevant calculator pages flag these in their per-page limitations sections.
• Closing costs and origination fees.Refinance break-even math depends heavily on these. The headline "monthly savings" figure ignores them; you have to recover them inside your time-in-loan horizon for refinancing to actually pencil.
• Lender-specific application rules. Some servicers apply borrower-initiated extras to future-month payments rather than current principal. The calculator assumes principal-only application; you usually have to instruct the servicer in writing.
• Risk-adjusted investment comparisons. When you compare prepayment to investing, the prepayment side returns a guaranteed APR-equivalent; the investing side returns an expected value with variance. Our math does not adjust for risk, sequence-of-returns, or tax-loss harvesting.

Each calculator page also carries its own "Where this calculator falls short" section listing the loan-type- specific cases.

Review and update process

Each calculator and guide carries a per-entry publishedAt and (when applicable) lastModifieddate sourced from a registry, not from the build timestamp. That means the "updated" date you see reflects an actual material edit — a content change, a corrected number, a new section — not a routine deploy.

Standing review cadence:

• FOMC weeks — the rate-outlook page and any guide that quotes a current rate are reviewed within a week of each FOMC meeting.
• Quarterly— every calculator's default values are sanity-checked against the latest Federal Reserve G.19, Freddie Mac PMMS, and SBA averages. Defaults shift up or down to keep the first paint realistic.
• On regulation change — when a relevant rule changes (PMI cancellation thresholds, SBA prepayment penalty schedule, FHA MIP terms), the affected calculator and guide are updated immediately and the date stamp bumped.

Corrections process and conflict-of-interest disclosures are in editorial policy.

Implementation reference

For developers and the math-curious: every formula above is implemented in plain TypeScript and unit-tested. The core amortization function lives in lib/calculator/amortization.ts; the multi-debt cascade is in lib/calculator/multi-debt.ts. Both have property-based tests covering the edge cases (zero APR, already-paid-off, lump sum exceeding balance, the 600-month safety cap). The tests are part of the build pipeline — anything that ships passes them.