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Estimate the monthly payment on a fixed-rate amortizing personal or auto loan from amount, annual interest rate, and term in months.

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Result

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The formula

A standard amortizing loan charges interest on the declining balance while keeping the payment level. With monthly rate r and n months, the payment formula is the same mathematical form used for fixed-rate mortgages.

M = P × [r(1+r)^n] / [(1+r)^n − 1]

Worked example

  1. P = $20,000, annual rate 6%, term 60 months
  2. Monthly rate r = 0.06 ÷ 12 = 0.005; n = 60
  3. M ≈ $386.66

Result: Payment ≈ $386.66/mo

How loan payments are calculated

This model assumes a fixed rate, equal monthly payments, and no optional fees inside the payment.

Amortization

Each payment covers that month’s interest first; the rest reduces principal. Early payments are interest-heavy; later payments retire more principal.

APR vs note rate

The note rate feeds this formula. APR may include certain fees so you can compare offers. A lower note rate with high fees can still be expensive — compare APR and total cost.

Term trade-offs

Longer terms lower the monthly payment but usually raise lifetime interest. Extra principal payments (when allowed) cut interest by shrinking the balance earlier.

Interesting facts

Amortization front-loads interest

Early payments on a standard amortizing loan are mostly interest; later payments retire more principal as the balance shrinks.

APR includes more than the rate

APR folds in certain fees so you can compare lenders. The note rate alone can hide origination costs.

Extra principal helps

Even modest extra principal payments early on cut total interest because they reduce the balance that keeps accruing interest.

Term length trade-off

A longer term lowers the monthly payment but raises lifetime interest. A shorter term costs more per month and less overall.

Prepayment rules

Some loans charge prepayment penalties. Read the contract before planning an early payoff.

Frequently asked questions

Enter principal, annual interest rate, and term in months. We apply the standard amortization formula for a fixed monthly payment.

Principal, interest rate, and term length. Rate and term changes often move the payment more than people expect.

The math is the same family of formulas. Mortgage pages often discuss taxes, insurance, and 15/30-year norms; this page is aimed at personal and auto-style terms in months.

No. Origination fees, insurance, and taxes are separate unless your lender rolls them into the principal.

References

  1. What is APR? — Consumer Financial Protection Bureau Clear distinction between note rate and APR.
  2. Shopping for a loan — U.S. Federal Trade Commission Consumer tips for comparing installment credit.