Interest Rate Calculator
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- Formula shown
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Results
Borrowing $25,000.00 and paying $500.00 a month for 60 payments implies an interest rate of 7.42% a year
| Year | Payments | Principal | Interest | Balance |
|---|---|---|---|---|
| 1 | $6,000.00 | $4,288.89 | $1,711.11 | $20,711.11 |
| 2 | $6,000.00 | $4,618.18 | $1,381.82 | $16,092.94 |
| 3 | $6,000.00 | $4,972.75 | $1,027.25 | $11,120.19 |
| 4 | $6,000.00 | $5,354.54 | $645.46 | $5,765.65 |
| 5 | $6,000.00 | $5,765.65 | $234.35 | $0.00 |
This is the interest rate on the amount borrowed. If the loan has fees, the APR will be higher; use the APR calculator to include them.
How to use the interest rate calculator
- Enter the loan amount: the money you actually borrow, after any down payment or trade-in.
- Enter the regular payment. Include principal and interest only, not insurance, taxes or add-on products paid through the loan.
- Choose how often you pay and enter the term in years or months.
- Read the annual rate, the effective annual rate and the total interest, with a year-by-year repayment table at that rate.
How the rate is found
Annual rate = i × payments per year
Effective annual rate = (1 + i)payments per year − 1
PMT is the payment, n the number of payments and i the interest rate per payment period. This is the standard present-value-of-an-annuity formula used for car loans, personal loans and mortgages: the loan amount equals the value today of all the payments you will make.
There is no way to rearrange the formula to get i on its own, so the calculator solves it numerically. It starts from a guess and refines it with Newton's method, falling back to bisection, until the payments discount back to the loan amount within a tiny fraction of a cent. Spreadsheet RATE functions and financial calculators work the same way.
Worked example
A dealer offers a $25,000 car loan at $500 a month for 60 months, but doesn't state the rate.
- Total of payments: 60 × $500 = $30,000, so the interest is $5,000.
- Solving $25,000 = $500 × [1 − (1 + i)−60] ÷ i gives i = 0.6183% a month.
- The annual rate is 0.6183% × 12 = 7.42%, an effective annual rate of 7.68%.
- A second offer of $420 a month for 72 months works out at 6.48%. The rate is lower, yet the total interest rises to $5,240.00 because you pay for a year longer.
Implied rate on a $20,000, 5-year loan
Each extra $25 a month on the same loan means a higher rate. With no interest at all, the payment would be $333.33.
| Monthly payment | Interest rate | Total interest |
|---|---|---|
| $350.00 | 1.94% | $1,000.00 |
| $375.00 | 4.73% | $2,500.00 |
| $400.00 | 7.42% | $4,000.00 |
| $425.00 | 10.01% | $5,500.00 |
| $450.00 | 12.5% | $7,000.00 |
| $475.00 | 14.92% | $8,500.00 |
Interest rate, effective rate and APR
- The interest rate shown first is the nominal annual rate: the rate per payment period times the number of payments a year. Loan documents usually quote this.
- The effective annual rate includes compounding between payments, so it is a little higher.
- The APR also counts fees and finance charges you pay to get the loan. If you paid an origination fee, the APR calculator shows how much it adds.
Tips
- If the result is far higher than you expected, check whether extras such as warranties, gap insurance or service plans were rolled into the payment. They raise the payment and so the implied rate.
- A negative result means the payments add up to less than the loan. Usually the term or payment was typed in wrongly.
- Compare offers on both the rate and the total interest. A longer term can cost more in total even at a lower rate, as the worked example shows.
- To see how the rate changes your savings instead of a loan, try the compound interest calculator, or solve any payment problem with the finance calculator.
Frequently asked questions
How do I find the interest rate on a loan if I only know the payment?
Enter the amount borrowed, the payment and the number of payments, and the calculator solves the loan formula for the rate. A $25,000 loan repaid at $500 a month for 60 months has an interest rate of 7.42% a year.
Why is there no simple formula for the interest rate?
The loan formula, amount = payment × [1 − (1 + i)^−n] ÷ i, cannot be rearranged to isolate i. Calculators and spreadsheets (the RATE function) solve it by trial and improvement, which this tool does to well under a cent of accuracy.
What is the difference between the interest rate and the effective annual rate?
The interest rate is the monthly rate times 12. The effective rate includes compounding over the year. For the $25,000 loan at $500 a month for 5 years, the rate is 7.42% and the effective annual rate is 7.68%.
Is a lower rate always the cheaper loan?
Not always. $25,000 at $420 a month for 72 months works out at 6.48%, lower than 7.42% for $500 a month over 60 months, but it costs $5,240 in interest instead of $5,000 because you pay for an extra year.
Does this calculate APR?
It gives the interest rate on the amount you borrow. If you paid fees to get the loan, the APR is higher because it treats the fees as part of the cost; the APR calculator works that out.