Interest Rate Calculator
The Interest Rate Calculator determines real interest rates on loans with fixed terms and monthly payments. For example, it can calculate interest rates in situations where car dealers only provide monthly payment information and total price without including the actual rate on the car loan.
Loan Information
Enter your loan information to calculate the interest rate
- Enter Loan Amount: Input the total amount borrowed or financed
- Set Loan Term: Specify the length of the loan in years and months
- Input Monthly Payment: Enter the fixed monthly payment amount
- Calculate: Click calculate to determine the interest rate and total costs
Loan Payment Formula
Where: PMT = Monthly Payment, P = Principal (loan amount), r = Monthly interest rate, n = Number of payments
Interest Rate Calculation
Since the interest rate cannot be solved algebraically from the payment formula, this calculator uses the Newton-Raphson numerical method to iteratively solve for the rate that produces the given payment amount.
Total Interest Calculation
When would I use this calculator?
This calculator is useful when you know the loan amount, payment, and term, but need to find the interest rate. Common scenarios include car loans where dealers quote monthly payments without clearly stating the APR.
Is this the same as APR?
The calculated rate is the periodic interest rate. For loans with additional fees, the APR would be higher. This calculator assumes no additional fees beyond the stated payment amount.
How accurate are the results?
The calculator uses advanced numerical methods to solve for interest rates with high precision. Results are accurate to several decimal places for standard loan scenarios.
What if I get unusual results?
Verify that your inputs are realistic. Very low payments relative to loan amount may result in negative interest rates, while very high payments may indicate calculation errors in the original loan terms.