Rate implied by cash flows
APR is solved by finding the monthly rate whose present value of all scheduled payments equals net proceeds after upfront finance charges. The rate is then multiplied by 12 for an annual percentage. Unlike a nominal note rate, it makes a withheld charge visible in the borrowing cost.
The default proceeds and payments
With $10,000 financed, $300 in upfront charges, and 36 payments of $320, net proceeds are $9,700 while total payments are $11,520. Solving the discounted-payment equation produces an estimated 11.53% APR.
Payment-timing assumptions
The solver assumes equal monthly payments and that the fee is paid from proceeds at the start. It treats every payment as exactly one month apart and does not include a first period that is unusually short or long.
Why a percentage shortcut fails
Do not divide total charges by the amount financed and call that APR. Timing matters: a charge withheld on day one affects the cost of every dollar received, while the same dollar amount paid later has a different present-value effect.
Costs excluded from this APR
Optional products, late fees, variable rates, taxes, compounding conventions, and charges excluded by a particular disclosure rule are not included. The output is an estimate of the cash-flow pattern entered, not a substitute for a regulated disclosure.
Checking an annual-cost disclosure
Use this page to sense-check whether an offer's payment and net proceeds agree with its stated annual cost. Compare loans only after their payment timing, fees, and amount actually received are expressed on the same basis.
A present-value check
The $320 payment multiplied by 36 is $11,520, but the borrower receives only $9,700 after the fee. The gap is not spread evenly through time: the fee is withheld before the first payment, which is why the solved APR is higher than a simple total-charge percentage. Preserve the actual first payment date when comparing a disclosure that uses an odd initial period.
Use the same cash-flow convention for every offer
One lender may collect a fee at closing while another adds it to the balance. Both can be compared, but only after the amount received and every scheduled payment are entered in the convention that actually applies.
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It is an educational estimate, not financial, tax, or legal advice.