A payment quote can hide the interest rate. “Only $400 a month for 60 months” sounds affordable, but the number that tells you whether it is a good deal is the rate behind it. This interest rate calculator works backward from the amount borrowed, the payment and the term to find the rate per payment, the APR and the effective annual rate — and shows how sensitive that rate is to the payment.
How to use the interest rate calculator
- Enter the loan amount — the price financed, not including any down payment.
- Enter the regular payment and how often it is made.
- Enter the term in months or years.
- If a lump sum is due at the end (a balloon or residual), enter it as the balance due at the end.
- Read the APR, the effective annual rate, total interest and the schedule.
Interest rate formula
The rate i per payment is the one that makes the payments, plus any final balance B, exactly repay the loan P:
There is no closed-form solution for i, so the calculator uses Newton’s method, refining a guess until the two sides match to many decimal places. Then:
where p is the number of payments per year.
Worked example
You borrow $20,000 and repay $400 a month for 60 months.
Total paid: 400 × 60 = $24,000, so total interest is $4,000.
Solving 20,000 = 400 × (1 − (1 + i)−60) ÷ i gives i = 0.618341% a month.
APR = 0.618341% × 12 = 7.42%; effective annual rate = 1.0061834112 − 1 = 7.678%.
If the same $20,000 instead had payments of $300 a month for 60 months plus $8,000 due at the end, the rate would be 8.27% APR.
Small payment changes, big rate changes
For the $20,000, 60-month loan:
| Monthly payment | APR | Total interest |
|---|---|---|
| $350 | 1.937% | $1,000 |
| $375 | 4.735% | $2,500 |
| $400 | 7.420% | $4,000 |
| $425 | 10.006% | $5,500 |
| $450 | 12.504% | $7,000 |
Each extra $25 a month adds about 2.5 to 2.8 percentage points to the rate. That is why it pays to negotiate on rate and price, not on monthly payment.
Using the result
Compare with other offers
Once you know the implied APR, compare it with rates from your bank or credit union. If a dealer’s payment implies 12% and your credit union offers 7%, financing elsewhere saves money even before negotiating the price.
Watch for add-ons
If the payment includes extended warranties or other products rolled into the loan, the amount financed is higher than the price you agreed to. Enter the actual amount financed to see the real rate.
Fees change the picture
This calculator finds the rate implied by the payment. If you also paid fees up front, the APR calculator includes them. To go the other direction — payment from a rate — use the loan calculator.
Estimates only. Lenders' disclosed APRs follow Regulation Z and may differ slightly because of payment rounding or irregular first periods.
Frequently asked questions
How do I find the interest rate from a payment?
Set the loan amount equal to the present value of the payments and solve for the rate per period. Because the rate cannot be isolated algebraically, it is found numerically. A $20,000 loan repaid with 60 monthly payments of $400 carries an APR of about 7.42%.
Why would I need to calculate the rate myself?
Some offers quote only a payment — a dealer's monthly figure, store financing, rent-to-own or a private loan. Working out the implied rate lets you compare the offer with a bank or credit union loan. US lenders must also disclose the APR under the Truth in Lending Act, so you can check their figure.
What is the difference between the APR and the effective annual rate here?
The APR is the rate per payment multiplied by the number of payments a year, as used in US disclosures. The effective annual rate compounds that periodic rate over a year. At 0.618341% a month, the APR is 7.42% and the effective rate is 7.678%.
What if the payments add up to less than the loan?
Then the implied rate would be negative, which means you would repay less than you borrowed. Check the inputs — the payment, the number of payments or a balloon amount may be missing.