Two loans, both "7%," can cost very different amounts — the difference hides in fees. APR is the repair: it re-prices the loan as if the fees were interest, giving one honest number to compare offers with.
How the calculation works
First, the monthly payment is computed the normal way from the quoted rate on the full amount. But you didn't really borrow the full amount — fees came off the top. So the calculator solves (by bisection, invisibly and deterministically) for the interest rate that would produce your exact payment on the net proceeds. That solved rate is the APR.
Worked example
$20,000 over 5 years at a quoted 7% costs $396/month. With an $800 origination fee you effectively received $19,200 for the same payment stream — an APR of about 8.7%. The fee turned a 7% loan into nearly a 9% one.
Term length changes everything about fees
Fees amortize over the life of the loan, so short terms concentrate the pain. The same $800 fee on a 30-year term barely nudges APR; on a 3-year loan it adds multiple points. Rule of thumb: the shorter the loan, the more suspicious of fees you should be — and points paid to "buy down" a mortgage rate only pay off if you keep the loan long enough.
Using APR well
APR is built for comparing like-for-like terms. Across different term lengths it can mislead — a longer loan may show a lower APR yet cost far more total interest, which the loan calculator makes visible. For revolving debt where fees are rare but compounding bites, see the credit card payoff calculator.
For information only; lender APR disclosures may include different fee sets.