LaTeX
PMT=P\frac{r(1+r)^n}{(1+r)^n-1}Variables
- P: principal
- r: periodic rate
- n: number of payments
- PMT: payment
How to use this formula
Calculates the fixed payment for a fully amortizing loan.
Important notes
- The formula excludes fees and changing rates.
- Use the payment frequency to convert the nominal rate correctly.
Quick example
A monthly mortgage uses monthly r and total monthly payment count n.
Applicability, worked calculation, and verification
Assumptions and domain checks
- For the Level Loan Payment, every denominator must be nonzero, and the numerator and denominator must remain correctly grouped.
- Match the interest rate to the compounding period, convert percentages to decimals, and keep cash-flow timing consistent.
Worked example
A monthly mortgage uses monthly r and total monthly payment count n.
Common mistakes
- When copying Level Loan Payment, keep the complete numerator and denominator grouped; a missing brace or parenthesis changes the result.
- Verify the result of Level Loan Payment with a known case, inverse operation, dimensional check, or independent calculation before publishing it.
Continue the workflow
Use Level Loan Payment in your own work
- Check the domainMatch the variables and assumptions to the problem before substituting values.
- Copy the exact notationPreserve grouping, signs, and exponents in
PMT=P\frac{r(1+r)^n}{(1+r)^n-1}. - Edit or convertOpen the expression in the LaTeX editor, then export it for your document or web page.
Review and verification
Last reviewed: 2026-07-23
Automated quality check: Kept noindex until the missing evidence is supplied.
Formula references
- Algebra and Trigonometry 2eOpenStax, Rice University — Reviewed algebra, functions, sequences, trigonometry, and analytic geometry definitions and examples.
Frequently asked questions
What is the Level Loan Payment used for?
Calculates the fixed payment for a fully amortizing loan.
Can I copy this formula as LaTeX?
Yes. Copy PMT=P\frac{r(1+r)^n}{(1+r)^n-1} or open it in the LaTeX editor.
What should I check before using it?
Confirm that each variable, unit, domain restriction, and assumption matches the problem.