formula
Loan Formula Explained
Complete Loan formula reference with variables, units, and examples.
PMT = P × [r(1+r)ⁿ] ÷ [(1+r)ⁿ − 1]
This reference explains the Loan formula used by our free Loan Calculator. Use it to understand variables, units, and common mistakes before you calculate.
The formula
PMT = P × [r(1+r)ⁿ] ÷ [(1+r)ⁿ − 1]
Variables and units
- P — Loan amount ($)
- r — Monthly interest rate (decimal)
- n — Number of payments (months)
Worked example
Inputs: $25,000 personal loan, 8% APR, 5-year term
- r = 0.08/12 = 0.006667
- n = 60
- PMT ≈ $507.35/month
Result: Monthly payment ≈ $507; total interest ≈ $5,441
When to use this formula
Use this formula when you need a quick loan estimate with values you already know. Our Loan Calculator applies the same relationship automatically so you can verify handwritten work.
Common mistakes
- Ignoring origination fees in true cost comparison
- Choosing longest term for lowest payment without checking total interest
- Missing prepayment penalty clauses
Frequently asked questions
What formula does the Loan Calculator use?
It uses: PMT = P × [r(1+r)ⁿ] ÷ [(1+r)ⁿ − 1]. Enter your values and the calculator returns the result with the same relationship.
Can I use different units?
Check the calculator field labels for expected units. Convert inputs before calculating if your data uses different units.
Is the Loan Calculator free?
Yes. It runs entirely in your browser with no account required.
Try the calculator
Loan Calculator