When to use this calculator
Find the implied nominal annual interest rate from principal, monthly payment and payment count. Assumes equal month-end payments and a fully repaid loan, with no balloon or fees. This is a nominal rate, not a statutory APR. Negative implied rates and nominal rates above 1,200% are outside this model. Rounded payments can change the inferred result.
Explore the loan & repayment calculators for other questions in this topic. For a related calculation, use the Loan Payment Calculator: Estimate a fixed monthly repayment for a fully amortising loan.
Use payments that fully clear the loan
This solver assumes equal month-end payments and no remaining balance after the final payment. A balloon loan or irregular payment schedule requires a different model. At zero interest, all payments sum to principal. If their sum is smaller than principal, the supported non-negative-rate model has no solution.
PUTTING IT INTO PRACTICE
Loan Interest Rate: a worked example
The values below are an illustrative example, not a recommendation. Replace them with measurements or assumptions that match your question.
| Input | Example value |
|---|---|
| Loan principal | 1,200 |
| Monthly payment | 100 |
| Number of monthly payments (integer) | 12 |
| Result | 0 % nominal annual |
- Check the input labels and enter the example values above.
- Apply the relationship: Solve payment = principal × monthly rate/[1 − (1 + monthly rate)^(−months)]; nominal annual rate = monthly rate × 1200..
- The result is 0 % nominal annual, rounded for display.
How to interpret your result
Assumes equal month-end payments and a fully repaid loan, with no balloon or fees. This is a nominal rate, not a statutory APR. Negative implied rates and nominal rates above 1,200% are outside this model. Rounded payments can change the inferred result.
Use a fixed-rate amortising model for loans repaid by equal monthly instalments. An interest-only payment leaves the principal outstanding. Fees and contractual APR calculations require more than the interest rate alone.
Frequently asked questions
Is the result the loan’s advertised APR?
Not necessarily. The output annualises a solved monthly rate by multiplying it by twelve. Fees, payment dates and local APR definitions can produce a different advertised figure.
Does a lower monthly payment mean a cheaper loan?
Not necessarily. Extending the term can lower payments while increasing total interest. Compare both monthly affordability and overall cost.
When is the loan interest rate calculator useful?
Find the implied nominal annual interest rate from principal, monthly payment and payment count. Assumes equal month-end payments and a fully repaid loan, with no balloon or fees. This is a nominal rate, not a statutory APR. Negative implied rates and nominal rates above 1,200% are outside this model. Rounded payments can change the inferred result.
How do I use the loan interest rate calculator?
Enter loan principal, monthly payment, number of monthly payments (integer). The result updates automatically. Use the units shown beside each input; the example values illustrate the method.
Which formula does this calculator use?
Solve payment = principal × monthly rate/[1 − (1 + monthly rate)^(−months)]; nominal annual rate = monthly rate × 1200..
What should I check before using the result?
Assumes equal month-end payments and a fully repaid loan, with no balloon or fees. This is a nominal rate, not a statutory APR. Negative implied rates and nominal rates above 1,200% are outside this model. Rounded payments can change the inferred result.
How are results rounded?
Scalar numbers display up to six decimal places, with scientific notation for very large or small values. Text, fraction, date and schedule outputs use the format described on the tool. Intermediate calculations use JavaScript floating-point arithmetic. Keep sensible precision for your measurements.
Further reading
For background on this topic, see OpenStax: loan payment relationships ↗. This is a topic reference, not an external review or endorsement of this tool.
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