An interest rate calculator finds the annual rate on a loan when you know the amount borrowed, the monthly payment and the term. $10,000 repaid at $200 a month for 60 months is about 7.42%.
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How to use the interest rate calculator
- Enter the loan amount you receive.
- Enter the monthly payment and number of months.
- Read the estimated annual rate.
How the interest rate calculator works
The interest rate calculator works backward from a loan. You enter the amount borrowed, the monthly payment and the number of months, and it finds the annual rate that makes the standard payment formula match your payment. There is no closed formula for the rate, so the tool uses bisection: it tries a rate, computes the payment, and halves the search range 80 times until the payment matches.
- Payment = P × r(1 + r)n ÷ ((1 + r)n − 1), with r = annual rate ÷ 12
- The tool searches annual rates from 0% to 100%
Interest rate calculator worked example
A $10,000 loan repaid at $200 a month for 60 months costs $12,000 in total. The interest rate calculator finds an annual rate of about 7.42%, because a 7.42% rate on $10,000 over 60 months gives a $200 payment. Scaling the loan and payment together, as in the $30,000 row, gives the same rate.
| Principal | Payment | Months | Annual rate |
|---|---|---|---|
| $10,000 | $200 | 60 | 7.42% |
| $5,000 | $450 | 12 | 14.45% |
| $200,000 | $1,300 | 360 | 6.77% |
| $30,000 | $600 | 60 | 7.42% |
Rate versus APR
If you enter the amount you actually receive and the payment you actually make, the result is close to the APR, because Regulation Z defines APR as the cost of credit as a yearly rate, including certain fees. If fees were added to the loan balance, enter the cash you received rather than the balance to see the true cost. The rate shown is a nominal annual rate compounded monthly, which is how lenders quote APR.
When to use it
Use the interest rate calculator to check a dealer quote that only gives a payment, to compare a lease-to-own or buy-now-pay-later plan, or to compare two offers with different terms. The CFPB recommends comparing the total cost of credit, not only the monthly payment, because a longer term can lower the payment while raising the total interest.
Limits
- Total payments must be at least the principal, otherwise there is no positive rate.
- Very high rates are found too; the search widens until it brackets the payment.
- Balloon payments, irregular payments and payment-due-at-start loans are not modeled.
Estimates for education only, not financial advice. Your lender’s figures are final.
Look at the total cost too
The rate is only part of the story. Multiply the payment by the number of months and subtract the amount borrowed to see the total interest. In the 60-month example, $200 × 60 is $12,000, so you pay $2,000 of interest on $10,000. Stretching the same loan to 72 months at the same rate lowers the payment but raises the total interest. When a seller offers a choice between a lower price and a special rate, run the interest rate calculator on each offer and compare the totals.
Some offers advertise a low monthly payment by adding fees or add-on products to the balance. If the payment covers extras you did not want, the effective rate on the money you actually needed is higher. Enter the cash you receive in the principal field to see that higher rate. If it looks high, ask the lender for the APR in writing; Regulation Z requires them to disclose it.
Comparing loan offers
Gather the amount, payment and term from each offer, run the interest rate calculator for each one, and line up the results. A credit union, a bank and a dealer can quote very different rates for the same borrower. A lower rate on a shorter term usually wins on total cost, as long as the payment fits your budget.
Related converters and calculators
Related calculators:
- Loan calculator: payments
- Auto loan calculator: car loans
- Simple interest calculator: simple interest
- Compound interest calculator: growth
Sources
CFPB: Regulation Z § 1026.22, determination of APR; CFPB: What is amortization?; CFPB: Auto loans.
Formula and method
Bisection for annual rate R so that PMT(principal, R, months) = payment; the upper bound doubles until it brackets the payment (no 100% cap).
Inverse of the amortizing payment formula. Not APY and not an APR fee model.
Questions about this calculator
Is the result the APR?
It is close to the APR if you enter the cash received and the actual payment.
Why is there no formula?
The payment formula cannot be solved for the rate directly, so it is searched numerically.
What if payments total less than the loan?
The tool shows an error because no positive rate fits.
Does it handle balloon loans?
No, only level monthly payments.
What is the highest rate it finds?
There is no 100% cap; very high rates are solved too.
Check the assumptions and units before relying on a result. Financial, tax and health estimates do not replace advice for your individual circumstances.
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