APR Calculator — the effective rate after fees

How it works

Two steps, one forward and one backward. Forward: the monthly payment on the full loan at the note rate, M = P·r(1+r)ⁿ ⁄ ((1+r)ⁿ − 1). Backward: the fees came out of what the loan delivered, so the amount you effectively financed is P − fees; the APR is the rate at which your payment M amortizes that net amount over the same n months, found by the same bisection search the interest-rate calculator uses. With zero fees the two amounts coincide and the APR equals the note rate exactly; every fee dollar pushes the APR above it — the direction CFPB states outright: the APR reflects the rate plus the charges, and is usually higher than the interest rate. The total cost of borrowing sums every payment and subtracts what you actually received.

Worked example

The identity case rests on a published pair: at zero fees, a $250,000 loan at 6% over 30 years pays $1,498.88 a month (LibreTexts) and its APR is exactly the 6% note rate — nothing added, nothing hidden. Load the default $5,000 of fees onto this page's $300,000 loan at 6.5% and the same payment now amortizes only $295,000 of net proceeds: this calculator solves an APR of about 6.66%, its own computation for those inputs — the fees cost about a sixth of a percentage point, every year, for thirty years.

Frequently asked questions

What is the difference between the interest rate and the APR?

The interest rate prices the borrowing itself; the APR is a broader measure that folds in points, broker fees, and other charges paid to get the loan (CFPB), which is why it is usually higher. Two offers with the same note rate can carry very different APRs purely on fees.

How is the APR computed here?

This page computes it by the amortization method: the payment on the full loan at the note rate, then solving for the rate at which that payment amortizes the loan minus the fees. That recovered rate is the APR — the cost of the money you actually walked away with. (A lender's disclosed APR follows Regulation Z's prescribed method, which can differ in which fees it includes.)

Why does the APR matter more than the rate when comparing offers?

Because it prices the whole package on one scale. A lender can quote a lower rate and recover it in fees; the APR exposes the trade by charging those fees against the amount you effectively received. Comparing APRs across offers with the same term is comparing total cost like-for-like.

Do more fees always mean a higher APR?

On this page's fee sweep, yes — strictly: each fee level raises the APR above the note rate, and the effect is larger on smaller loans and shorter terms, where the same dollars are a bigger share of the money received. The sweep makes the sensitivity visible for your own loan.

Is a lower APR always the better offer?

Not automatically: the APR assumes the loan runs to term. Fees are paid once, up front, while a rate difference accrues over years — sell or refinance early and a low-fee, higher-rate offer can win even with a higher APR. The mortgage-points calculator prices exactly that break-even.

What fees go into the fees field?

The charges paid to get the loan: discount points, origination and broker fees, and similar line items from your loan estimate. Costs you would pay regardless of financing — like a home's title insurance in some cases — are convention-dependent; your lender's disclosed APR states which items it includes.

How accurate is this, and what does it exclude?

The solve is exact for the inputs given. It excludes mortgage-insurance premiums, variable-rate features, and the issuer-specific inclusion rules for particular fee types that Regulation Z prescribes, so your lender's disclosed APR can differ slightly from the figure here — compare the inputs on the loan estimate if the two diverge.