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Result

The formula

Standard amortizing loan payment formula.

M = P × [r(1+r)^n] / [(1+r)^n − 1]

Worked example

  1. P = $20,000, r = 6%/12, n = 60
  2. Monthly payment ≈ $386.66

Result: Payment: $386.66/mo

How monthly payments are calculated

A standard amortizing loan keeps the payment amount fixed. Early installments are mostly interest; later ones pay down more principal.

Monthly rate and term

r is the annual rate divided by 12. n is the number of months. P is the amount borrowed. The formula returns the fixed payment M.

APR vs. nominal rate

US consumer loans often advertise APR, which folds in certain fees. This tool treats the rate you enter as a nominal annual interest rate — always compare the APR and fee schedule on the actual offer (CFPB Loan Estimate guidance for mortgages and similar disclosures elsewhere).

Amortization shape

With a fixed payment, interest is charged on the remaining balance each month. As principal falls, the interest portion shrinks and more of each payment reduces the balance.

What we do not model

Interest-only periods, prepayment penalties, insurance add-ons, and mortgage-specific rules (escrow, PMI) are omitted. For a home loan, use the mortgage calculator.

Interesting facts

Amortization

Early payments are mostly interest; later payments pay down more principal.

Shorter terms cost less overall

A 36-month auto loan usually has a higher monthly bill than a 60-month loan for the same rate, but you pay less total interest because the balance shrinks faster.

Rate shopping beats brand loyalty

US borrowers often save by comparing credit unions, banks, and online lenders. A one-point APR difference on a multi-year loan can outweigh small fees.

Extra principal cuts the schedule

Paying more than the minimum toward principal shortens the loan and reduces total interest, provided the lender applies the extra payment to principal rather than future installments.

Frequently asked questions

Principal, interest rate, and loan term length. Fees and insurance can raise the cash you actually pay even when the formula payment is unchanged.

It is a principal-and-interest estimate only. Taxes, insurance, and fees are not included unless you fold them into the amount or rate yourself.

Interest is charged on the full outstanding balance. Early on, that balance is largest, so interest takes most of a fixed payment.

It works for a simple amortizing estimate, but home loans often add escrow, PMI, and points. Prefer a dedicated mortgage calculator for housing.

References

  1. What is a Loan Estimate? — Consumer Financial Protection Bureau Explains key loan cost disclosures in consumer credit.
  2. Shopping for a loan — Consumer Financial Protection Bureau Compare APR, fees, and term length before signing.

Estimates only — not financial advice.

Last reviewed: 2026-07-01 — Reviewed by: Editorial Team

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