Interest Rate Calculator
Find the interest rate on a loan given the amount, payment, and term.
Examples
Auto Loan Rate
Mortgage Rate Check
Frequently Asked Questions
What is the difference between APR and APY?
How does Newton's method work?
What if my payment is too low?
Quick Tips
Double check your inputs. Ensure units match (e.g., inches vs cm).
How to Use This Calculator
Enter your loan amount, monthly payment, and the total number of monthly payments. Click Calculate to find the annual interest rate (APR) on your loan. This is useful when you know your payment details but need to determine the underlying interest rate.
Understanding the Formula
Uses Newton's method to iteratively solve: PMT = PV * r * (1+r)^n / ((1+r)^n - 1), where PMT = monthly payment, PV = loan amount, r = monthly rate, n = number of payments.
Examples
Auto Loan Rate
If you borrowed $25,000 and pay $477.53/month for 60 months, the calculator determines your APR is approximately 5.50%.
Mortgage Rate Check
A $300,000 mortgage with $1,610.46/month payment over 360 months (30 years) has an APR of approximately 4.50%.
Frequently Asked Questions
What is the difference between APR and APY?
APR (Annual Percentage Rate) is the nominal annual rate without compounding. APY (Annual Percentage Yield) accounts for the effect of monthly compounding and is slightly higher than APR.
How does Newton's method work?
Newton's method is an iterative numerical technique that starts with an initial guess and refines it using the function and its derivative until it converges on the correct rate with high precision.
What if my payment is too low?
The minimum possible payment equals the loan amount divided by the number of months (a 0% rate scenario). If your payment is lower than this, no positive interest rate can produce that payment schedule.