Real APR on any loan
The stated rate ignores origination, points, and anything else rolled into the loan that functions like interest. The effective rate doesn’t. Bisection solver finds the IRR that makes the cash flow honest.
Inputs
The principal the loan documents say. Not the cash you receive.
The headline rate. The number at the top of the page.
As % of stated principal. Deducted from the funded amount. = $1,250.
Each point = 1% of principal upfront. = $0.
Application, processing, prepaid interest, anything else due at funding.
Output panel
Assumptions and formula →
Monthly payment is computed on the STATED principal using the STATED APR (standard fixed-rate amortization, the same formula the lender uses). This is what you actually pay every month.
Cash received = stated principal − origination − discount points − other upfront costs. The fees are deducted at funding (or rolled in but conceptually identical) so you walk away with less than the loan documents say.
Effective APR is the internal rate of return that equates the present value of the actual payment stream to the cash you actually received: cashReceived = PMT × (1 − (1+r)^−n) / r. No closed form; we bisect r in [0, ∞) to sub-cent precision. Annualized × 12.
Regulatory note.The Truth in Lending Act requires lenders to disclose an APR that includes certain “finance charges” — origination usually is, points sometimes are, third-party fees often aren’t. The TILA APR can still understate this honest IRR, especially for non-standard fee structures. This calculator counts every dollar you don’t walk away with as a finance charge, by design.
Read the long-form derivation: Calculator 2 — Real APR on any loan →