Method / assumptions / examples
How this calculation works
The result is deterministic: the same measurements always return the same estimate. Here is the relationship and where real-world results can differ.
Formula
M = P × i × (1 + i)ⁿ ÷ ((1 + i)ⁿ − 1)
For monthly payments, P is principal, i is the nominal annual interest rate divided by 12, and n is the number of monthly payments. At a zero rate, payment is principal divided by the number of payments. Principal and term use algebraic rearrangements of the same equation; the rate is found with a bounded numerical search. Each schedule row rounds only for display, then reconciles the last payment to the remaining balance.
Worked example
Examples
The fixed principal-and-interest payment is approximately $477.42 per month before fees or other costs.
A $12,000 balance paid over 24 months requires exactly $500 per month.
If the payment does not cover one month of interest, the calculator rejects the term solve because the loan will not amortize.
Common mistakes
What to check before using the result
- Use the amount actually financed as principal. Subtract any down payment and exclude fees paid separately.
- Compare total interest as well as the monthly payment. A longer term can lower the payment while increasing the total cost.
- Extra principal can shorten the payoff schedule substantially, but confirm that your agreement applies extra money to principal without a prepayment penalty.
- Treat the calculated rate as a nominal annual rate, not an APR. APR can include fees and follows jurisdiction-specific disclosure rules.
FAQ
Frequently asked questions
Is this monthly payment the amount a lender will quote?
It is the fixed principal-and-interest payment for the values entered. A lender may add fees, insurance, taxes, or other charges.
Why is the last payment sometimes smaller?
A whole number of regular payments can slightly exceed the remaining balance. The schedule reduces the final payment to reconcile the balance to zero.
Does an extra payment reduce next month's required payment?
This model keeps the regular payment unchanged and applies the extra amount to principal, shortening the payoff period. Actual loan servicing rules can differ.
Is the solved interest rate an APR?
No. It is the nominal annual rate implied by principal, payment, and term. APR calculations can include finance charges and jurisdiction-specific rules.
Primary references