Interest Rate Calculator: Find the Rate on a Loan
Know the amount borrowed, the monthly payment and how many payments there are? Work backward to the interest rate the loan is charging.
A loan's interest rate is the monthly rate at which the payments, discounted back to today, add up exactly to the amount borrowed, multiplied by 12. There is no algebra shortcut for it, so it is found by trying rates until the two sides match. Borrowing $25,000 and paying $483.32 a month for 60 months works out to a monthly rate of 0.5%, an APR of 6%, and just under $4,000 of interest in total.
This calculator gives an estimate for general education only and is not financial advice. It assumes equal monthly payments, equal monthly periods and no balloon payment, fees or rate changes, so it can differ from the APR in your loan disclosure, which is the figure that counts. Before refinancing or signing a loan, check the lender's disclosure and consider asking a qualified financial professional.
Interest rate (APR)
6.000%
- Monthly rate
- 0.500%
- Effective annual rate (compounded monthly)
- 6.168%
- Total of payments
- $28,999.20
- Total interest
- $3,999.20
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About the Interest Rate Calculator
Most loan calculators start from a rate and give you a payment. This one runs the other direction, which is useful when a dealer or lender quotes only a monthly figure, or when you want to check what an existing loan is really charging. It uses the standard present-value equation for a loan with equal monthly payments: the amount borrowed equals the payment times one minus (1 + i) to the power of minus n, all divided by i, where i is the monthly rate and n the number of payments. Because i appears on both sides of that equation in a way that cannot be rearranged, the calculator narrows in on it by repeated halving until the two sides agree to many decimal places. The nominal APR is twelve times the monthly rate, which is the figure a loan contract quotes. The effective annual rate compounds the same monthly rate over twelve months, so it is a little higher, 6.168% for a 6% APR. The calculator also shows the total you will pay and how much of it is interest. If the payments do not add up to at least the amount borrowed, no rate can make them repay the loan, and the calculator says so.
Frequently asked questions
How do I find the interest rate from a monthly payment?+
You need three numbers: the amount borrowed, the monthly payment and the number of payments. Enter them and the calculator solves the loan equation for the monthly rate, then multiplies by 12 for the APR. For $25,000 repaid at $483.32 a month over 60 months, the answer is 6%.
Why is there no simple formula for the rate?+
The payment formula can be solved for the payment, the amount or the term, but the rate shows up both as a multiplier and inside an exponent, so it cannot be isolated. Spreadsheets use the same trial-and-error approach in their RATE function, and so does this calculator.
What is the difference between APR and the effective annual rate?+
APR is the monthly rate times 12, with no compounding. The effective annual rate lets each month's interest earn interest, so a 0.5% monthly rate becomes 6% APR but 6.168% effective. Loan contracts quote APR; the effective rate is useful for comparing against savings yields.
Why might my result differ from the rate on my loan documents?+
If fees were added to the loan or taken out of the amount you received, the rate on the note and the APR can differ. Enter the amount you actually received to see the cost including fees, or the full loan balance to see the note rate. A first payment that falls more or less than a month after signing also shifts the official figure slightly.
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