Interest Rate Calculator
Find the interest rate on a fixed-term loan from the loan amount, term, and monthly payment
By Waqar Mushtaq · Last updated:
Dealers, lenders, and buy-now-pay-later offers often quote a loan as "just $400 a month for 60 months" without putting the interest rate front and center. This interest rate calculator works backwards from the numbers you do know -- how much you're borrowing, how many months, and the monthly payment -- to find the interest rate the loan actually charges. Alongside the rate it shows the effective annual rate, the total interest over the life of the loan, a year-by-year chart of how the balance falls and the interest adds up, and how much the rate would change if the payment were a little lower or higher.
Solving the Loan Payment Formula for the Rate
Iterative (bisection, ~200 steps)M = monthly payment · P = loan amount · r = monthly interest rate · n = number of monthly payments
This is the standard formula for a fixed-payment, fully amortizing loan -- the same one used by the mortgage and amortization calculators on this site. Normally you know the rate and solve for the payment. Here the payment is known and the rate is the unknown, and there's no algebraic way to isolate r. Instead the calculator searches for it numerically: the payment rises steadily as the rate rises, so it repeatedly halves the range of possible rates until the computed payment matches yours to well under a cent.
Example: $20,000 borrowed for 60 months at $400 a month.
- Total of payments: 60 × $400 = $24,000, so total interest is $4,000
- The monthly rate that makes the formula give $400 is about 0.6183%
- Annual rate: 0.6183% × 12 = 7.420%; effective annual rate (1.006183¹² − 1) = 7.678%
Edge cases:
- If the payments add up to exactly the loan amount, the rate is 0% (the formula itself is undefined at r = 0, so this is handled as a special case).
- If the payments add up to less than the loan amount, no positive interest rate fits -- check that the term and payment were entered correctly.
The rate found here is the loan's interest rate, not its APR. If you also paid origination fees or points, the APR Calculator folds those into a single cost-of-borrowing figure.
Use Cases
Auto Loans Quoted by Monthly Payment
Car dealers frequently negotiate on the monthly payment rather than the rate. Plug in the amount financed, the term, and the payment you were quoted to see the rate you're really being charged, then compare it against rates from your bank or credit union.
Checking a Lender's Disclosed Rate
If you know the loan amount, term, and payment from your paperwork, you can confirm the stated interest rate is consistent with them -- a mismatch can mean fees were rolled into the loan amount.
Personal Loans, Furniture Financing, and Pay-Over-Time Offers
Installment offers ("12 easy payments of $90 on a $1,000 purchase") hide the rate in the payment. Working it out (14.45% in that example) makes it easy to compare against simply using a credit card or saving up.
Comparing Offers With Different Terms
A longer loan with a smaller payment can carry a higher rate and much more total interest. Running each offer through the calculator puts them on the same footing: rate, total interest, and how quickly the balance comes down.
Frequently Asked Questions
How do I find the interest rate on a loan if I only know the payment?
You need three numbers: the amount borrowed, the number of monthly payments, and the monthly payment. The loan payment formula links those to the interest rate, but it can't be rearranged to solve for the rate directly, so calculators like this one find it numerically by trying rates until the payment matches.
What is the difference between the interest rate and the APR?
The interest rate is the cost of borrowing the principal itself. The APR also folds in lender fees such as origination charges and points, so it's usually higher than the interest rate. This calculator finds the interest rate implied by the payment on the amount actually borrowed; use the APR calculator if you also paid upfront fees.
What is the effective annual rate shown under the result?
Loan rates are quoted as a nominal annual rate -- the monthly rate times 12. Because interest compounds monthly, the true annual cost is slightly higher: (1 + monthly rate)^12 − 1. On a 7.42% loan that works out to about 7.68%.
Why does the calculator say the payment is too low?
If the number of payments times the monthly payment is less than the loan amount, you'd be paying back less than you borrowed, which would require a negative interest rate. That usually means the term or payment was mistyped, or that a balloon payment is due at the end, which this calculator doesn't model.
Does this work for mortgages?
Yes, for the principal-and-interest part of a fixed-rate mortgage payment. Leave out property taxes, homeowners insurance, and PMI -- those are often included in a monthly mortgage payment but aren't part of the loan's interest calculation.
Methodology
The formula above is implemented as a standalone module covered by unit tests, so its worked examples are re-checked on every change to the site. It is verified against the authoritative sources listed below.
Not financial advice. This calculator is a general informational tool and cannot account for your individual circumstances. See the terms of use.
Maintained by Waqar Mushtaq. Spotted a result that looks wrong? Report it and it becomes a failing test.