Interest Rate Calculator

What this interest rate calculator does

This calculator finds the interest rate on a fixed-rate loan when you know the amount borrowed, the term, and the monthly payment. It solves for the monthly rate that makes the present value of the payments equal to the loan amount, then reports the nominal annual rate.

The result is useful when a lender quotes a monthly payment but does not clearly state the rate, or when you want to compare offers with different terms.

How to use this calculator

1. Enter the loan amount.
2. Enter the term in years and months.
3. Enter the monthly payment.
4. Click Calculate.

The default example uses a $32,000 loan, a 3-year term, and a $960 monthly payment. The result is a 5.065% nominal annual rate.

Interest rate formula

For a fixed-rate loan with equal monthly payments:

Loan amount = PMT × (1 − (1 + r)^−n) / r

PMT is the monthly payment, r is the monthly interest rate, and n is the number of monthly payments. The calculator solves this equation for r. Because r appears in both a denominator and an exponent, the solution is found with a numerical search rather than a single algebraic step.

The nominal annual rate is:

Nominal APR = monthly rate × 12

The effective annual rate is:

Effective APR = (1 + monthly rate)^12 − 1

What the results include

• Interest rate: the nominal annual rate.
• Monthly rate: the rate used for each payment period.
• Effective APR: the rate after accounting for monthly compounding.
• Total payments: the monthly payment multiplied by the number of months.
• Total interest: total payments minus the loan amount.
• Amortization schedule: the monthly and yearly split between interest and principal.
• Balance chart: the remaining balance, cumulative interest, and cumulative payments over time.

Assumptions and limitations

The calculator assumes a fixed interest rate, equal monthly payments, and a fully amortizing loan. It does not include origination fees, closing costs, insurance, taxes, prepayment penalties, or extra payments. A payment that is too low to repay the loan over the entered term will produce an error rather than a rate.

Frequently asked questions

Is the result the same as the APR on my loan offer?

Not necessarily. The nominal rate here is based only on the loan amount, term, and payment. A lender's APR may include fees and other costs, so it can be higher than this result.

Why can't the calculator find a rate?

If the total of all payments is less than the loan amount, the loan is not repaid at any non-negative rate. If the payment is too high for the term, the rate may also fall outside the range that can be solved reliably.

Does the calculator include extra payments?

No. Every payment is assumed to be the same amount and made on schedule. Extra principal payments change both the payoff time and the effective cost.

Can I use this for a mortgage?

Yes, as long as the mortgage has a fixed rate and equal monthly payments and you enter the loan amount, term, and principal-and-interest payment. Property taxes, insurance, and association dues should not be included in the payment.

Source

References:

• Consumer Financial Protection Bureau — Loans
• Consumer Financial Protection Bureau — What is an APR?

Disclaimer

This calculator is for informational purposes only. It is not a loan offer or financial advice. Confirm the rate, fees, and repayment terms with the lender before signing.