Interest Rate Calculator
Find the implied interest rate on a loan given the loan amount, monthly payment, and term using Newton-Raphson iteration.
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Annual Interest Rate
Monthly Rate
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APY
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Total Interest
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No solution found. Check that the monthly payment is large enough to repay the loan.
What is Interest Rate Calculator?
The interest rate calculator works backwards from a known loan amount, monthly payment, and term to find the implied annual interest rate. This is useful when you've been quoted a monthly payment and want to verify the effective rate, or when comparing loan offers where the rate isn't clearly disclosed.
How to use
- 1 Enter the original loan amount.
- 2 Enter the monthly payment amount.
- 3 Enter the loan term in months.
- 4 The implied monthly rate, annual rate, and APR are calculated using numerical iteration.
Formula
Example calculation
You borrowed $10,000 and pay $222/month for 48 months. The solver finds r ≈ 0.833%/month → 10% annual rate. Total paid: $10,656. Total interest: $656.
Frequently asked questions
Why use numerical iteration instead of a direct formula?
The interest rate cannot be isolated algebraically from the amortization formula. Newton-Raphson iteration converges to the solution in a few steps with high accuracy.
What is the difference between interest rate and APR?
For a simple installment loan with no fees, the nominal annual rate and APR are identical. APR becomes higher than the rate when origination fees or other charges are included.
How do I use this to check a car dealership's offer?
Enter the car's financed amount (price minus down payment), the quoted monthly payment, and the loan term in months. Compare the resulting rate to rates from banks or credit unions.
What if the calculator shows 'No solution'?
This occurs when the monthly payment is too low to ever pay off the loan (less than the first month's interest) or when inputs are inconsistent. Verify your numbers.
Is this the same as APY?
No. APY (Annual Percentage Yield) accounts for compounding frequency. For monthly-compounding loans, APY = (1 + r)¹² − 1, which is slightly higher than the nominal annual rate.