APR vs. EAR — the distinction
The APR you are usually quoted is a nominal annual rate: what you would pay if interest were applied just once a year. The EAR (effective annual rate) is the actual annualized return or cost once compounding is taken into account — the single annual rate that produces the same year-end balance as compounding at the stated frequency.
- Compounding frequency matters. For the same nominal rate, more frequent compounding yields a higher EAR. Monthly compounding on a 6% nominal rate averages out higher than 6.00% once a year — the delta is pure compounding, not a hidden charge.
- An upfront fee behaves like an interest-rate jump. When a fee is subtracted from proceeds, the balance still grows at the stated rate but you received less up front — so the effective cost lands above the compounding-only EAR.
- Comparing instruments. Quotes are best compared on the same basis — the EAR is the apples-to-apples number. APR figures may bundle other charges or follow a statutory definition, so this tool is a pure-math model, not a statement of how any specific APR is disclosed or regulated.
Formulas used
r = nominal annual rate · m = periods per year · f = fee ÷ principal (0 ≤ f < 1) · e ≈ 2.71828