How we calculate

Every number on loan.tools comes from the formulas below. No black boxes.

Draft — under independent mathematical review.

Monthly payment (principal & interest)

The standard fixed-rate amortization formula:

M = P · r / (1 − (1 + r)⁻ⁿ)

P = amount borrowed · r = annual rate ÷ 1200 (monthly rate as a decimal) · n = term in months. If the rate is 0%, the payment is simply P ÷ n.

The amortization schedule

Each month, interest accrues on the remaining balance first; the rest of the payment reduces principal:

interest_m = balance_m−1 · r  principal_m = M − interest_m  balance_m = balance_m−1 − principal_m

This is why early payments are mostly interest: the balance is largest at the start. The crossover marked on our charts is the first month where principal_m ≥ interest_m.

Extra payments

Monthly, yearly, and one-time extra payments are added to principal_m in the month they occur. The payment M stays the same, so the loan ends early; the interest saved is the difference between the two schedules' total interest.

PMI (private mortgage insurance)

Applied when the down payment is under 20%. Monthly PMI is the annual PMI rate times the original loan amount, divided by 12. It's charged until the balance reaches 80% of the purchase price:

PMI/month = loan · rate_PMI / 12, charged while balance > 0.80 · price

Lenders differ on exact removal rules (78% automatic termination, appraisal-based removal). We use the 80%-of-original-price convention.

Property tax & insurance estimates

The "typical estimates" button uses 1.10% of the home price per year for property tax and 0.35% for homeowners insurance. ZIP lookups map to state-level averages (California uses 1.15%, the effective rate for a new purchase under Prop 13, because the state average misleads buyers). County rates vary — verify yours.

Refinance break-even

break-even months = ⌈ closing costs / (old payment − new payment) ⌉

If the new payment isn't lower, there is no break-even. Lifetime comparison uses total interest remaining on the current loan versus total interest on the new loan plus closing costs.

Auto loans

Most states tax the price minus your trade-in; manufacturer incentives reduce the amount financed but are usually still taxed:

tax = max(price − trade-in, 0) · rate_tax  financed = price + tax − down − trade-in − incentives

A few states tax the full price or cap the trade-in credit — check your state's rule.

Auto leases & money factor

A lease payment is depreciation plus a finance charge:

payment = (cap − residual)/n  +  (cap + residual) · MF

cap = negotiated (capitalized) cost after reductions · residual = MSRP × residual % · MF = money factor. Approximate APR = MF × 2400. Dealers often quote "2.5" to mean 0.00250. Working backwards from a quoted payment: MF = (payment − depreciation) / (cap + residual).

Rates

Live rates are the Freddie Mac Primary Mortgage Market Survey weekly averages (30-year and 15-year fixed), fetched from FRED. They're national survey averages, not offers.

How we keep it honest

An automated test suite checks the exact code these pages run against published example loans and closed-form results — payment amounts, total interest, PMI drop-off months, extra-payment payoffs, lease money factors — on every change.

Rounding: we display dollars rounded to the nearest dollar; schedules compute in full precision. Your lender's numbers may differ slightly due to payment dates, escrow, and fees. This is math, not financial advice.