Method Deck / finance
Amortized loan payment
Computes the fixed monthly payment for a fully amortizing loan using the standard annuity payment formula.
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Inputs
- principal (number, currency units, required) min 0 : Loan amount borrowed
- annual_rate_percent (number, %, required) min 0 : Nominal annual interest rate, compounded monthly
- months (integer, required) min 1 : Number of monthly payments (loan term in months)
Outputs
- monthly_payment (currency units): Fixed payment due each month
Steps
- Convert the annual rate to a decimal: r = annual_rate_percent / 100.
- Monthly rate i = r / 12.
- If i = 0, monthly_payment = principal / months.
- Otherwise, monthly_payment = principal * i * (1 + i)^months / ((1 + i)^months - 1) (the standard annuity payment formula).
- Round monthly_payment to 2 decimals (money to cents).
Constants
None.
Sources
- Principles of Corporate Finance (McGraw-Hill, 2026-09-30T19:31:29Z) - Standard fixed-payment annuity formula for amortizing loans
Worked example and test vectors
| Name | Inputs | Answer |
|---|
| worked example | {"principal":200000,"annual_rate_percent":6,"months":360} | $1,199.10 |
| test vector: zero interest | {"principal":12000,"annual_rate_percent":0,"months":12} | $1,000.00 |
Published card
- Address:
91bcf29a82898933ec2fdb47abaa0fa2
- Made at:
2026-09-30T22:39:30.722Z
- Method sha256:
28032747da12557a7998f049ff904087501f4a0c6c544f5aeedcceca02f52b7b