What are the assumptions of the Loan formula?

Fixed interest rate for the entire loan term. Equal monthly payments (standard amortization). No prepayment or balloon payment. Loan fees are either included in the principal or paid separately (not in the payment formula).

What are the limitations of Loan?

This formula does not account for variable rates (some private student loans, HELOCs). Origination fees, late fees, and prepayment penalties are not included. For credit cards, payments are not fixed — minimum payments can extend the loan indefinitely.

Methodology

How we calculate loan payments

Our methodology for the Loan calculator: the formula, step-by-step calculation, authoritative sources, and limitations. Reviewed quarterly.

Formula

M = P × [r(1+r)ⁿ] / [(1+r)ⁿ − 1]

Step-by-step

1
Determine the loan principal (P): the amount borrowed.
2
Determine the monthly interest rate (r): divide the APR by 12.
3
Determine the number of monthly payments (n): years × 12.
4
Compute (1 + r)ⁿ: the total compounding factor.
5
Apply the formula: P × [r(1+r)ⁿ] / [(1+r)ⁿ − 1]. The result is the monthly payment.
6
Multiply the monthly payment by n and subtract P to get total interest paid.

Authoritative sources

Every claim on this page is backed by an authoritative source.

Assumptions

What we take to be true when applying this formula.

Fixed interest rate for the entire loan term.
Equal monthly payments (standard amortization).
No prepayment or balloon payment.
Loan fees are either included in the principal or paid separately (not in the payment formula).

Limitations

What this method does NOT capture.

This formula does not account for variable rates (some private student loans, HELOCs).
Origination fees, late fees, and prepayment penalties are not included.
For credit cards, payments are not fixed — minimum payments can extend the loan indefinitely.

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Last reviewed: 2026-06-15 • Reviewed by: CalcxApp editorial team