How do I use the Interest Rate Calculator?

Enter the required values, then calculate. The Interest Rate Calculator shows results, formulas, and step-by-step work when available. No account is required.

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How it works

When a dealer or lender quotes a payment but not a rate, this tool inverts the amortization formula. The result is a fixed compound monthly rate, expressed as an annual percentage. Simple interest, variable rates, and fee-inclusive APR are not modeled.

A = P · i(1+i)^N / ((1+i)^N − 1) → solve for i, APR = 12i

When to use

Use this tool when you need to: default check: {principal} repaid at {payment}/mo for 3 years is about 5.065%.

How to use this tool

Enter your values in the fields above.
Review the formula and any mode options for your problem.
Read the result and the step-by-step solution.

Default check: {principal} repaid at {payment}/mo for 3 years is about 5.065%.

Frequently asked questions

What is the Interest Rate Calculator?: When a dealer or lender quotes a payment but not a rate, this tool inverts the amortization formula. The result is a fixed compound monthly rate, expressed as an annual percentage. Simple interest, variable rates, and fee-inclusive APR are not modeled.
How do I use the Interest Rate Calculator?: Enter the required values, then calculate. The Interest Rate Calculator shows results, formulas, and step-by-step work when available. No account is required.
What formula does the Interest Rate Calculator use?: A = P · i(1+i)^N / ((1+i)^N − 1) → solve for i, APR = 12i

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Interest Rate Calculator

Recover the fixed annual rate of a loan from the amount, term, and monthly payment.

How it works

What this interest rate is

The interest rate is the cost of borrowing, as a percentage of the remaining principal. This calculator finds the fixed annual rate of an amortizing loan when you know the amount, the monthly payment, and the term — for example when a quote lists the payment but not the rate.

How the rate is solved

Each month, interest is charged on the balance and the rest of the payment reduces principal. The level payment that pays the loan off in N months is A = P · i(1+i)^N / ((1+i)^N − 1), with i = r/12. This tool solves that equation for r. If the payments exactly equal the principal, the rate is zero. If they cannot cover the principal, there is no solution.

Compound, fixed, and variable

The result is a compound monthly rate, not simple interest (which would charge only on the original principal). It is also a single fixed rate for the whole term. Variable or adjustable rates that change with an index are not modeled.

APR and the real rate

Advertised APR can package fees into the rate; this calculator uses only the loan amount and the stated payment, so it is the contract rate, not a fee-inclusive APR. The real rate is the nominal rate minus inflation: nominal = real + inflation. Shop multiple lenders — the same payment can hide a different term or extra fees.

How it works

A = P · i(1+i)^N / ((1+i)^N − 1) → solve for i, APR = 12i

When to use

Use this tool when you need to: default check: {principal} repaid at {payment}/mo for 3 years is about 5.065%.

How to use this tool

Enter your values in the fields above.
Review the formula and any mode options for your problem.
Read the result and the step-by-step solution.

Default check: {principal} repaid at {payment}/mo for 3 years is about 5.065%.

Frequently asked questions

What is the Interest Rate Calculator?: When a dealer or lender quotes a payment but not a rate, this tool inverts the amortization formula. The result is a fixed compound monthly rate, expressed as an annual percentage. Simple interest, variable rates, and fee-inclusive APR are not modeled.
How do I use the Interest Rate Calculator?: Enter the required values, then calculate. The Interest Rate Calculator shows results, formulas, and step-by-step work when available. No account is required.
What formula does the Interest Rate Calculator use?: A = P · i(1+i)^N / ((1+i)^N − 1) → solve for i, APR = 12i

Browse categories