Transparent method
The formula
Worked example
Example inputs
How to interpret the result
Reverse-solving for the rate implied by a principal, payment and number of payments reveals the loan's real cost even when a lender advertises the deal in terms of payment size alone. The implied rate is what actually determines whether an offer is competitive, not the payment figure being marketed.
Before you rely on it
What to check
Compare the reverse-solved implied rate against current market rates and against the lender's disclosed APR, since a mismatch between the two can signal fees folded in elsewhere.
The common error
Where people go wrong with loan interest rate calculator
Judging a loan offer by its advertised monthly payment alone without reverse-solving for the implied rate. A payment that looks manageable can be hiding a rate well above market once the actual math gets run.
Sensitivity evidence
How monthly payment changes the estimated annual interest rate
| Monthly payment | Estimated annual interest rate | Total interest | Total payments |
|---|---|---|---|
| $400 | 0.000% | -$1,000 | $24,000 |
| $450 | 3.1% | $2,000 | $27,000 |
| $500worked example | 7.4% | $5,000 | $30,000 |
| $550 | 11.5% | $8,000 | $33,000 |
| $600 | 15.4% | $11,000 | $36,000 |
Every input, tested
Which input moves the estimated annual interest rate most
| Input | Tested from | To | Estimated annual interest rate at each end | Swing |
|---|---|---|---|---|
| Number of payments | 45.0 months | 75.0 months | 0.000% to 13.9% | 13.9% (187%) |
| Monthly payment | $450 | $550 | 3.1% to 11.5% | 8.4% (114%) |
| Amount borrowed | $22,500 | $27,500 | 12.0% to 3.5% | 8.5% (114%) |
Two variables at once
Estimated annual interest rate by monthly payment and amount borrowed
| Monthly payment \ Amount borrowed | $20,000 | $25,000 | $30,000 |
|---|---|---|---|
| $400 | 7.4% | 0.000% | 0.000% |
| $450 | 12.5% | 3.1% | 0.000% |
| $500 | 17.3% | 7.4% | 0.000% |
| $550 | 21.8% | 11.5% | 3.8% |
| $600 | 26.1% | 15.4% | 7.4% |
Step by step
The worked example, input by input
| Input | Value used |
|---|---|
| Amount borrowed | $25,000 |
| Monthly payment | $500 |
| Number of payments | 60.0 months |
| Estimated annual interest rate | 7.4% |
| Total interest | $5,000 |
| Total payments | $30,000 |
Where the inputs come from
The amount borrowed is what you receive, the monthly payment is the fixed amount scheduled each month, and the number of payments is the count of months in the term. Use these to back into a rate when a seller quotes only a payment, as sometimes happens with car or furniture financing. The result assumes the payment covers only principal and interest, so remove insurance or service contracts included in the quote.
When the result stops applying
A first payment delayed by more than a month, an odd first period or a balloon breaks the assumption. If the payment includes a fee, the true rate on the borrowed money is lower than the result suggests.
What to compare it with
Use the result to shop. If the implied rate is high, ask for the cash price and the financing terms separately, then compare with a bank loan at the same amount. The APR calculator can then add any upfront fees to the picture. This is also a good way to test rent-to-own, buy-here-pay-here and furniture plans, where the payment is advertised and the interest rate is not. A payment quote with no rate is worth translating before you agree.
People also ask
Frequently asked questions
Why solve for the rate instead of asking the seller?
Sellers sometimes quote a payment instead of a rate. Solving for the rate lets you compare the deal with a loan from a bank.
Is the result the same as APR?
Close, when there are no upfront fees. If fees exist, the APR is higher than the rate computed from the payment alone.
Can the rate come out negative?
If total payments are less than the amount borrowed, the loan implies a negative rate, which usually means the inputs are mismatched, for example a payment for fewer months.