Loan Interest Rate Calculator
Uncover the hidden annual interest rate on any financing contract. When lenders quote a monthly payment and tenure without stating the APR, solve for the true interest rate instantly.
Cash balance borrowed on paper
Contracted monthly installment
Number of monthly payments
Calculated true annual interest rate percentage
How to Use This Calculator
- Enter the total principal amount financed.
- Input the monthly installment payment requested by the lender.
- Specify the total term in months (e.g. 60 months for a 5-year loan).
- Instantly uncover the true contractual annual interest rate.
Formula & Calculation Methodology
Uses iterative numerical analysis (Newton-Raphson approximation) to solve the nonlinear root for periodic interest rate.
Worked Example
$20,000 borrowed at $450/month over 60 months
Frequently Asked Questions
Why do lenders quote monthly payments instead of interest rates?↓
Focusing consumers on an "affordable" monthly payment distracts from high underlying interest rates and extended repayment terms.
How does Newton-Raphson numerical analysis solve for interest rate?↓
Because the amortization formula has no algebraic closed-form solution for rate r, numerical solvers test successive approximations until the error is zero.
Does this calculate APR or nominal interest rate?↓
This calculates the nominal interest rate based on cash payments; if upfront fees were withheld from the loan, the true APR will be even higher.
What happens if payments are lower than zero-interest amortization?↓
If total payments (Payment × Months) are less than or equal to principal, the implied interest rate is 0%.
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Source Citation & Disclaimer
Informational tool only; not licensed tax, legal, or financial advice.