About the Interest Rate Calculator
This interest rate calculator works backwards from a loan you already have or have been offered. Enter how much you borrow, the fixed monthly payment and the number of payments, and it solves for the annual interest rate that makes those numbers add up — the same rate a lender would disclose as the note rate or APR when there are no upfront fees.
It is useful when a dealer, store or lender quotes only a monthly payment ("just $400 a month!"), when you are reviewing an old loan and cannot find the rate on the paperwork, or when a friend or family loan was agreed as a payment schedule rather than a rate. Knowing the rate lets you compare the offer with a credit union, bank or credit card on equal terms.
The calculation assumes a standard fully amortizing loan with equal monthly payments and monthly compounding. If you paid fees upfront, subtract them from the loan amount to see the true APR including fees.
With the default inputs, the annual interest rate (apr) is 7.42%. Change any value above to recalculate instantly.
How to use the interest rate calculator
- 1Enter the amount you borrowed (subtract any upfront fees to see the true APR).
- 2Enter the fixed monthly payment from your loan agreement or quote.
- 3Enter the total number of monthly payments.
- 4Read the annual interest rate and compare it with other offers.
Formula and method
There is no closed-form equation that isolates the rate in the loan payment formula, so the calculator solves it numerically. It repeatedly tries monthly rates, computes the payment each would require for your loan amount and term, and narrows in (by bisection) until the computed payment matches the payment you entered to a fraction of a cent.
The resulting monthly rate r is multiplied by 12 to give the nominal annual rate (APR), which is how US and most other lenders quote installment loans. The effective annual rate (APY) compounds that monthly rate over 12 months and is always slightly higher. If the total of all payments is not more than the loan amount, the rate is 0%.
- P
- Loan amount (principal)
- M
- Fixed monthly payment
- n
- Number of monthly payments
- r
- Monthly interest rate being solved for
Worked examples
$20,000 loan at $400/month for 60 months
Sixty payments of $400 total $24,000, so you pay $4,000 more than you borrowed. Solving the payment formula gives a monthly rate of about 0.618%, or 7.42% APR — 7.68% once monthly compounding is included.
$300,000 mortgage at $1,995.91 for 30 years
A $300,000 loan repaid over 360 payments of $1,995.91 corresponds to exactly a 7% mortgage rate. Across 30 years the borrower pays about $418,528 in interest.
$8,000 store financing at $250/month for 3 years
Thirty-six payments of $250 total $9,000 — $1,000 of interest on $8,000. That equals roughly 7.81% APR, a figure you can now compare directly with a bank or credit union loan.
Frequently asked questions
How do I calculate the interest rate on a loan?+
You need the loan amount, the monthly payment and the number of payments. Because the rate cannot be isolated algebraically in the amortization formula, it is found by trial and error — this calculator does that search automatically in a fraction of a second.
Is this the APR or the interest rate?+
If the loan amount you enter is the full amount you received with no fees, the result is both the note rate and the APR. If you paid origination or other fees, enter the loan amount minus those fees and the result becomes the APR including fees.
What is the difference between APR and APY?+
APR is the monthly rate multiplied by 12. APY (effective annual rate) accounts for monthly compounding, so it is slightly higher — a 7.42% APR equals about 7.68% APY.
What is a good interest rate on a personal loan?+
It depends on your credit score and the lender. Borrowers with excellent credit often see single-digit to low-teen APRs on personal loans, while fair or poor credit can push rates toward 30% or more. Always compare several offers using the APR.
Why does the calculator show 0%?+
If the total of all payments is equal to or less than the amount borrowed, no interest is being charged — or the payment is too small to pay the loan off in the number of months entered.
Results are estimates for educational purposes and are not financial advice. Rates, fees and terms vary — confirm with your lender or a licensed advisor before making decisions.