About this Interest Rate
Sometimes you know the monthly payment and the loan amount, but the interest rate is hidden or unclear (common with 'Buy Here Pay Here' car lots or rent-to-own). This tool solves for the interest rate so you can see the true cost of borrowing.
How to use this calculator
- Enter the Loan Amount (Principal).
- Enter the Loan Term (months or years).
- Enter the Monthly Payment.
- The tool calculates the implied APR.
Accuracy and testing
Review formula sources, default test cases, assumptions, unit handling, rounding rules, and changelog for this calculator.
How this calculator works
The formula for loan payments is P = (r*PV) / (1 - (1+r)^-n). Solving for 'r' (rate) algebraically is impossible, so this calculator uses the Newton-Raphson numerical method to estimate the rate with high precision.
Inputs explained
Loan Amount
The cash price of the item or the amount borrowed.
Monthly Payment
The amount you pay every month.
Understanding your results
The Interest Rate (APR) is the effective annual cost. If this number is high (e.g., >20%), reconsider the loan. The Total Interest Cost shows how much extra you are paying over the price.
Example scenarios
Car Loan
Borrow $20,000. Pay $400/mo for 60 months. Implied Rate: ~7.42%.
Bad Deal
Borrow $5,000. Pay $200/mo for 48 months. Implied Rate: ~34%. Total Cost $9,600 (nearly double).
Key Features
- Newton-Raphson Solver
- Total Cost Analysis
- Reverse Calculation
Things to Keep in Mind
Assumes a fixed rate and equal monthly payments. Does not work for interest-only loans or balloon payments.
Tips & Best Practices
- Use this to check dealer quotes. If the rate they quote doesn't match the payment, they might be hiding fees or add-ons.
- High rates (>30%) are often predatory. Check local usury laws.
Glossary of Terms
- Implied Rate
- The interest rate that mathematically connects the principal, payment, and term.
- Usury
- Lending money at unreasonably high rates of interest.