Interest Rate CalculatorFree online financial calculator — instant results, no sign-up
Find the rate on a loan from amount, payment and term.
Estimates only, based on the inputs and assumptions shown. This is not financial, investment, tax, or legal advice. Prices, rates and local rules may change; crypto scenarios do not predict returns. Confirm important decisions with a qualified professional.
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About the Interest Rate Calculator
This calculator determines the implied annual interest rate (APR) of a fixed-rate loan based on the borrowed principal, regular monthly payment, and loan term. Borrowers use it to evaluate financing offers, check car loan quotes, or verify stated interest rates against contractual terms.
- Loan amount
- The original principal amount borrowed, in dollars, typically ranging from $500 to $1,000,000+.
- Monthly payment
- The required monthly fixed payment amount, in dollars, which must be large enough to pay off the principal over the term.
- Term
- The total length of the loan repayment period, expressed in months (for example, 60 months for a 5-year loan).
Formula and method
Payment formula: M = P × (r × (1 + r)^n) / ((1 + r)^n − 1) Total Interest = (M × n) − P
- MMonthly payment
- PLoan principal amount
- nNumber of monthly payments (term in months)
- rMonthly interest rate (Annual Interest Rate ÷ 1200), solved via numerical iteration
Because the interest rate cannot be isolated algebraically from the standard amortization formula, the calculator uses a binary search algorithm running 100 iterations between 0% and 100% to approximate the annual interest rate to three decimal places. Total interest is then calculated by subtracting the principal from the cumulative payments (monthly payment multiplied by term).
Worked example
These are the calculator's starting values and the results it actually produces for them.
Inputs
- Loan amount30000 $
- Monthly payment600 $
- Term60 months
Results
- Interest rate7.42%
- Total interest$6,000.00
How to use the Interest Rate Calculator
- 1Enter the total borrowed principal amount, the agreed monthly payment, and the loan duration in months.
- 2The algorithm checks candidate interest rates between 0% and 100% using the standard loan payment equation.
- 3Through 100 successive bisection steps, it narrows down the exact annual interest rate that matches your payment.
- 4The total interest cost is calculated by multiplying the monthly payment by the term and subtracting the original loan amount.
Reading your result
The primary result displays the annual interest rate implied by your payment terms, showing the effective borrowing cost. The total interest figure shows the complete dollar surcharge paid above the original principal across the full loan duration.
Limitations
The calculation assumes fixed monthly compounding and level amortized payments throughout the loan. It does not account for upfront origination fees, dealer doc fees, balloon payments, or payment schedules that do not amortize fully within the specified term.
Common questions
Why isn't there a direct formula to solve for the interest rate?+
The standard amortization equation contains the interest rate both as a multiplier and inside an exponent, making it a transcendental equation. It has no closed-form algebraic solution, requiring numerical approximation methods like binary search.
What happens if my total payments are less than the loan amount?+
If the monthly payment multiplied by the number of months is less than the loan principal, the implied interest rate would be negative, which standard fixed-rate consumer loan algorithms cannot resolve.
Is the calculated interest rate the same as the APR on my loan disclosure?+
It represents the nominal interest rate based solely on payments and principal. A lender's disclosed APR may be higher if upfront financing fees, points, or closing costs were financed into the loan.
Does the calculator save my information?+
Calculations run in your browser. While signed in, inputs and results are automatically recorded in account history; saving a result creates a separate saved record.
Further reading
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Results are estimates for informational purposes and are not financial, medical or legal advice.