Quick answer
The interest rate is the rate i at which payment × (1 − (1 + i)^−n) ÷ i equals the loan amount, quoted as 12 × i. A $200,000 loan repaid with $1,199.10 a month over 30 years has an interest rate of 6% APR.
Enter the loan amount, monthly payment and term. The calculator solves for the rate.
Related tools: Real Interest Rate Calculator: Inflation-adjusted interest rate using the exact Fisher relation. Cash Back or Low Interest Calculator: Compare a cash rebate with a lower financing rate on a purchase. Auto Loan Calculator: Monthly car payment after down payment and trade-in.
How to use the Interest Rate Calculator
- Enter loan amount ($) (above 0).
- Enter monthly payment ($) (above 0).
- Enter term (years) (between 0 and 50).
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Loan amount | A number, in $ | > 0 |
| Monthly payment | A number, in $ | > 0 |
| Term | A number, in years | > 0, ≤ 50 |
Formula and method
Formula
Find i such that payment × (1 − (1 + i)^−n) ÷ i = loan amount; rate = 12 × i
IEEE-754 double precision; money shown to cents, rates to 4 decimals. Results are estimates, not financial advice.
Solved by bisection; the payments must at least repay the principal.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Loan amount = 200000; Monthly payment = 1199.1; Term = 30.
| Result | Value |
|---|---|
| Interest rate (APR) | 6% |
Example 2
Inputs: Loan amount = 15000; Monthly payment = 300; Term = 5.
| Result | Value |
|---|---|
| Interest rate (APR) | 7.4201% |
Example 3
Inputs: Loan amount = 10000; Monthly payment = 250; Term = 4.
| Result | Value |
|---|---|
| Interest rate (APR) | 9.2418% |
The first line is the headline result (interest rate (APR)). IEEE-754 double precision; money shown to cents, rates to 4 decimals. Results are estimates, not financial advice.
Why it needs iteration
The rate cannot be isolated algebraically, so the calculator finds it numerically by trying rates until the payments repay the loan. For the example, a 6% annual rate (0.5% a month) gives a payment of $1,199.10.
Checking a quote
Use this to check the rate implied by a quoted payment. Fees rolled into the loan are not included, so the true cost can be higher. The payments must repay at least the principal, or the calculator rejects the inputs.
How the result changes with loan amount
Holding every other input at the first worked example, this table changes only loan amount. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Loan amount | Interest rate (APR) |
|---|---|
| 100000 | 14.1796% |
| 200000 | 6% |
| 400000 | 0.5133% |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Monthly payment: entering "50" shows "The payments add up to less than the loan amount, so no non-negative rate fits." beside that field and no result.
- Loan amount: entering "0" shows "Loan amount must be greater than 0." beside that field and no result.
Choosing between the Interest Rate Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Real Interest Rate Calculator](/finance/real-interest-rate-calculator/) | nominal interest rate and inflation rate | Real interest rate |
| [Cash Back or Low Interest Calculator](/finance/cash-back-or-low-interest-calculator/) | price, down payment and cash rebate | Better choice |
| [Auto Loan Calculator](/finance/auto-loan-calculator/) | vehicle price, down payment and interest rate | Monthly payment |
| [Amortization Calculator](/finance/amortization-calculator/) | loan amount, interest rate and term | Monthly payment |
| [Loan Calculator](/finance/loan-calculator/) | loan amount, interest rate and term | Monthly payment |
Background: loans and mortgages
The interest rate is the cost of borrowing the principal; the APR also folds in certain fees, so a lower rate with high fees can have a worse APR. These calculators use the rate you enter and do not add fees, insurance or taxes, so add fees to the principal if you want to include them.
A fixed-rate loan is paid in equal instalments, early ones mostly interest. Extra payments go straight to principal, which shortens the loan and cuts interest; adjustable rates, escrow changes and prepayment penalties are not modelled.
Assumptions and limitations
- Payments must repay at least the principal
Results are estimates for planning, not financial advice. Lender terms, fees, taxes and rounding rules can change real figures, so confirm important numbers with your lender or a licensed adviser.
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for monthly payment and loan amount to confirm this.
Frequently asked questions
What is APR?
The yearly cost of borrowing as a rate, here 12 times the monthly rate.
Can it handle interest-only loans?
No, payments must repay principal.
Why does a shorter term raise the payment?
The principal is repaid faster.
What does the Interest Rate Calculator calculate?
Annual interest rate implied by a loan amount, payment and term. It returns Interest rate (APR).
What formula does the Interest Rate Calculator use?
Find i such that payment × (1 − (1 + i)^−n) ÷ i = loan amount; rate = 12 × i. Solved by bisection; the payments must at least repay the principal.
What do I need to enter in the interest Rate Calculator?
You enter Loan amount ($), Monthly payment ($) and Term (years).
How is the result rounded or limited?
IEEE-754 double precision; money shown to cents, rates to 4 decimals. Results are estimates, not financial advice. Payments must repay at least the principal.
What is an example of a interest Rate result?
With loan amount 200000, monthly payment 1199.1 and term 30, the interest rate (APR) is 6%.
Can I rely on this calculator for a decision?
Results are estimates for planning, not financial advice. Lender terms, fees, taxes and rounding rules can change real figures, so confirm important numbers with your lender or a licensed adviser. For this calculator in particular: Payments must repay at least the principal.
Related calculators
- Real Interest Rate Calculator — Inflation-adjusted interest rate using the exact Fisher relation.
- Cash Back or Low Interest Calculator — Compare a cash rebate with a lower financing rate on a purchase.
- Auto Loan Calculator — Monthly car payment after down payment and trade-in.
- Amortization Calculator — Full amortization schedule with optional extra monthly payments.
- Loan Calculator — Estimate your monthly loan payment, total interest and total cost.
- HELOC Calculator — Interest-only draw-period payment and the repayment-period payment of a home equity line.
Sources
- Standard time-value-of-money relations (e.g. Brealey, Myers & Allen, Principles of Corporate Finance)
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.