A loan quoted at 6.5% with $6,000 of fees is not a 6.5% loan. You pay interest on the full amount, but you never receive the full amount — the fees come out of it. The effective rate is the rate that makes the payments you actually make equal the money you actually got, and it is the only figure that compares two offers honestly.
Someone is comparing two loan offers with different rates and different fees and wants to reduce both to one number, rather than guessing which combination is cheaper.
Interest is charged on the full loan, but the fees are taken out before the money reaches you. On a $300,000 loan with $6,000 of fees you receive $294,000, and every monthly payment is calculated on $300,000. You are paying interest on money you never got.
The effective rate is what closes that gap. Discounting the 360 payments of $1,896.20 back at 6.695% a year gives $294,000 — the amount you actually received. So the loan costs 6.695%, not the 6.5% on the offer, and the difference is 0.195 percentage points.
That gap is not small money over a term. Interest plus fees on this loan come to $388,633.47, against $382,633.47 of interest alone. The $6,000 of fees is real, and the rate comparison is how you see it in the same units as the rate.
On a $300,000 thirty-year loan, each one per cent of the loan charged in fees adds very close to 0.097 percentage points to the effective rate. Half a per cent adds 0.048; two per cent adds 0.195; four per cent adds 0.397. The near-perfect doubling is not a coincidence — the fee is a fixed deduction against a fixed payment stream, so doubling it doubles its effect on the rate.
The term behaves differently, and this is the part that catches people. The same $3,000 fee — one per cent of the same $300,000 loan — adds 0.097 points over thirty years but 0.225 points over ten. The fee is identical and the loan is identical; only the number of payments it is spread across changes. Fewer payments means each one carries more of the fee, which shows up as a higher annual rate.
So a short-term loan with low fees can still be the more expensive one per year, and the effective rate is how you see that. Comparing a fifteen-year offer against a thirty-year offer on quoted rates alone compares two numbers that were never on the same footing.
This is the same idea as an APR and it is not the same number. A regulated APR has a definition written into law: it includes third-party closing costs, it has rules about which fees count, and it is disclosed on a form the lender is obliged to produce. What this page computes is the rate implied by the loan amount, the quoted rate, the term and the fees you enter — a narrower and more transparent calculation.
That narrower scope is deliberate. Third-party costs such as title insurance, appraisal and recording are largely the same whichever lender you pick, so including them muddies a comparison between offers without changing which one wins. Lenders sometimes quote an APR that includes them precisely because it makes a cheap loan look expensive next to a competitor's.
The honest limit is that this calculator knows nothing about the fees it is not told about. If a loan carries a prepayment penalty, an annual fee, or a rate that resets after a fixed period, none of that is in the arithmetic here and all of it changes the real cost. The effective rate is a better comparison than the quoted rate; it is not a substitute for reading the offer.
net proceeds = Σ payment ÷ (1 + i)^k for k = 1…N, solved for i, then × 12 × 100
This is the same shape as an internal rate of return: a known cash inflow today against a known stream of outflows later. There is no closed form for it, so it is solved by bisection. The present value falls steadily as the rate rises, which is what makes bisection safe here — and the answer is checked in the test suite by discounting the payments back at the reported rate and confirming they reproduce the net proceeds.
Quoted at 6.5%, the payment is $1,896.20 and the loan runs 360 months. With $6,000 of fees deducted, $294,000 actually reaches the borrower. Discounting those 360 payments back at 6.695% gives exactly $294,000, so the effective rate is 6.695% — 0.195 percentage points above the quoted rate. Interest plus fees over the term come to $388,633.47.
Set the fees to zero and the effective rate comes back as 6.5% — exactly the quoted rate — with $300,000.00 reaching the borrower. This is not a trivial result; it is the check that proves the calculation is sound. With nothing deducted, the present value of the payments must equal the loan amount, and the only rate at which that holds is the rate the payment was calculated from. If this case returned anything other than the quoted rate, the bisection would be solving the wrong equation.
The identical $300,000 loan and the identical $3,000 fee, over ten years instead of thirty. The money actually received is $297,000.00, and the payment is $3,406.44 across 120 of them. The effective rate comes out at 6.725%, a gap of 0.225 percentage points — more than double the 0.097 points the same fee costs over thirty years. Nothing about the fee changed. What changed is how many payments it has to be absorbed by, and that is the comparison a quoted rate hides.
The interest rate is what the lender charges on the balance. The effective rate is what you actually pay once the fees are accounted for, because the fees reduce the money you receive without reducing the money you repay. On a $300,000 loan at 6.5% with $6,000 of fees, the effective rate is 6.695% — the quoted rate is a real number, it is just not the whole cost.
It is the same idea and not the same number. A regulated APR includes third-party closing costs and follows a legal definition that governs which fees are counted. This calculator works from the fees you enter, which is narrower and more transparent — and it does not include anything you did not tell it about, such as a prepayment penalty or an annual fee.
Because the same fee is absorbed by fewer payments. Three thousand dollars spread across 360 payments adds about 0.097 points to the annual rate; spread across 120 payments it adds 0.225. The fee does not change — the number of payments carrying it does.
Compute the effective rate for each, using the same fee categories for both. That puts a low-rate/high-fee offer and a high-rate/low-fee offer on one scale. Leave out costs that are identical between the lenders, such as title and appraisal, because including them shifts both numbers without changing which is smaller.
No. Mortgage interest is often deductible in the United States, which lowers the real cost of borrowing, and the effective rate here is before any of that. The after-tax cost is a separate calculation and depends on your marginal rate and whether you itemise, which the calculator has no way to know.