Working backwards to the rate
Most loan calculators start with a rate and find the payment. This one runs the relationship in reverse: you supply what you borrowed, what you pay each month, and how many months the loan lasts, and it deduces the interest rate baked into those numbers.
There is no neat algebraic formula to isolate the rate, so the calculator searches for it. It repeatedly guesses a monthly rate, computes the payment that rate would produce, and narrows the guess until the computed payment matches yours. The matching monthly rate is then annualised into an APR.
When this is useful
Backing out the rate is handy when an offer quotes only a price and a monthly payment — common with dealer financing, rent-to-own arrangements, or "no interest" promotions that may hide a cost. Computing the implied rate lets you compare such deals on equal footing with ordinary loans.
It also helps you sanity-check a quote: if the implied APR is far higher than advertised, fees or an inflated price may be lurking in the payment.
Reading the output
The implied APR is the annual rate consistent with your figures. The total interest is simply all your payments added up minus the amount borrowed, and the chart shows how that interest compares with the principal.
Limitations
The result assumes a simple, fixed, fully-amortizing loan with equal monthly payments. If the real loan has fees, a balloon payment, irregular instalments or a variable rate, the implied APR here will differ from the lender’s stated APR. Use it as a comparison tool, not an official figure.
Formula
find r where P·r / (1 − (1+r)⁻ⁿ) = payment; APR = r·12·100Frequently asked questions
- Why must the payments add up to more than the loan?
- If total payments do not exceed the amount borrowed, there is no positive interest rate that fits, so the inputs are inconsistent.