Interest Rate Calculator
A dealer quotes you a monthly payment but not the rate? This interest rate calculator works backwards from the numbers you know. In loan mode, enter the amount borrowed, the monthly payment and the number of payments to find the interest rate. In growth mode, enter a starting and an ending value to find the compound rate per month or per year. You get the periodic rate, the nominal annual rate and the effective annual rate.
Updated
Results
- Nominal annual ratePeriodic rate × periods per year, as APRs are quoted
- Effective annual rateIncludes compounding, like APY
- Total interest
Results are estimates. See the methodology below.
How to use the calculator
Loan mode
- Amount: the money you actually receive. If fees are taken out of the loan, enter the net amount.
- Payment: the fixed monthly payment.
- Number of periods: how many monthly payments, e.g. 60 for a five-year loan.
Growth mode
- Amount: the starting value.
- Future value: the ending value.
- Number of periods and whether they are months or years.
How the calculator works
In loan mode the calculator finds the monthly rate i that makes the standard amortizing payment formula balance:
Amount = Payment × (1 − (1 + i)^−n) ÷ i
There's no algebraic shortcut for i, so it's solved numerically by bisection to many decimal places. In growth mode the rate has a direct formula:
i = (Future value ÷ Amount)^(1/n) − 1
From the periodic rate the calculator derives:
- Nominal annual rate = i × 12 for monthly periods. This is how APRs on loans are quoted.
- Effective annual rate = (1 + i)^12 − 1, which includes compounding. It's the same idea as the APY on savings.
- Total interest = payment × n − amount (loan) or future value − amount (growth).
With yearly periods in growth mode, all three rates are the same.
Worked examples
| Case | Per month | Nominal annual | Effective annual | Interest |
|---|---|---|---|---|
| $10,000 loan, 24 × $450 | 0.6251% | 7.501% | 7.764% | $800 |
| $25,000 car loan, 60 × $495 | 0.5831% | 6.997% | 7.226% | $4,700 |
| $1,000 loan, 12 × $90 | 1.2043% | 14.452% | 15.449% | $80 |
| $5,000 grows to $5,200 in 12 months | 0.3274% | 3.928% | 4.000% | $200 |
The $1,000 loan shows why the rate matters more than the dollar cost: $80 of interest on $1,000 sounds like 8%, but because you repay the principal month by month, you only have the full amount for the first month. The actual rate is 14.452% a year.
Growth mode with years: $10,000 that becomes $15,000 in 5 years grew at 8.447% a year, compounded. The total gain is $5,000, or 50%, but that is not 10% a year.
Interest rate, APR and APY
The rate you find in loan mode reflects every dollar between what you receive and what you repay. If the amount you entered is the net amount after fees, the result is close to the loan's APR, which the CFPB describes as the interest rate plus additional lender fees. If you enter the gross amount, it shows only the interest. Compare loans using the nominal annual rate, which matches how APRs are quoted, and savings products using the effective rate, which matches APY.
Frequently asked questions
How do I find the interest rate on a car loan from the payment?
Use loan mode: enter the amount financed, the monthly payment and the number of months. For a $25,000 loan paid with 60 payments of $495, the rate is 6.997% a year. Compare it with the APR on your contract.
What's the difference between nominal and effective annual rate?
The nominal rate is the monthly rate times 12. The effective rate compounds the monthly rate over 12 months, so it's always a bit higher when the rate is positive. A monthly rate of 0.6251% is 7.501% nominal and 7.764% effective.
Is the result the same as the APR?
Close, but not always identical. Under Regulation Z the APR is a measure of the cost of credit expressed as a yearly rate, it includes certain fees, and lenders determine it from the loan's exact payment schedule. This calculator assumes equal monthly payments starting one month after you receive the money.
Why do I get an error saying there's no solution?
If the payments add up to less than the amount borrowed, no positive interest rate can explain them. Check that you entered the monthly payment and the full number of payments.
Can I use it for investment returns?
Yes. Growth mode gives the compound annual growth rate between two values. It ignores deposits and withdrawals in between, so use it only when the money was left alone for the whole period.
Sources
This calculator gives estimates for comparison only and is not financial advice. The APR and payment schedule on your loan documents are the official figures.