Solve for the unknown interest rate given loan amount, payment, and term. Compare rates and see APR vs nominal rate differences.
Loan Details
Enter any 3 values to solve for the interest rate
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Annual Interest Rate
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Monthly Rate
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Annual Rate
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Monthly Rate
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Total Interest
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Total Cost
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Principal
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Monthly Payment
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Loan Term
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Solved Rate (Annual)
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Total Paid
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Total Interest
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FAQ
How is the interest rate solved?
The calculator uses iterative Newton-Raphson bisection to find the rate r that satisfies the payment formula: P = L × [r(1+r)^n] / [(1+r)^n−1]. Since there's no closed-form solution for r, numerical approximation is used.
What is APR vs interest rate?
The interest rate (nominal rate) is the cost of borrowing principal only. APR (Annual Percentage Rate) includes fees like origination costs and points, giving a more complete cost measure. Always compare APRs when shopping for loans.
What is a good mortgage interest rate?
This depends on the market environment. Historically, 30-year fixed rates averaged ~8% since 1971. Sub-4% rates (2020-2021) were unusually low. As of 2024, rates of 6.5-7.5% are considered typical.