What is the difference between APR and interest rate?

The interest rate prices the borrowing and produces your monthly payment. The APR prices the whole deal, adding the fees you paid to get the loan and expressing them as extra rate. If a loan has no fees the two are identical; the bigger the fees, the wider the gap, and the gap is what the advertised rate hides.

How is APR calculated?

By solving for the rate at which your payment stream is worth exactly the cash you received, the loan amount less any fees deducted at closing. There is no formula to rearrange, so it is found numerically. This calculator halves the interval until the answer is accurate to a twentieth of a basis point.

Should I pay discount points?

Only if you will keep the loan long enough to recover them. Points are a fee now for a lower rate later, and the calculator shows the effect directly: shorten the term and watch the APR climb while the fees stay the same. If you expect to move or refinance within a few years, points rarely pay for themselves.

Is the lowest APR always the best loan?

Not automatically. APR assumes you keep the loan for its full term, so it flatters a loan with heavy up-front fees if you plan to leave early. It also only compares fairly across identical terms. Use it to see through advertised rates, then check the total cost of credit, shown above, against how long you actually expect to hold the loan.

Why does my Loan Estimate show a different APR?

Because lenders include a specific set of charges in the finance charge and exclude others. Third-party costs the lender does not require, and prepaid escrow, are generally left out; mortgage insurance is generally put in. Enter only the lender-required fees here and the figures should converge.

Does this work for a car loan or personal loan?

Yes, the arithmetic is identical for any level-payment loan with fees taken from the proceeds. Note that short terms magnify the effect of a fee, so a $500 fee on a three-year personal loan moves the APR far more than the same fee on a mortgage. For the payment itself, use the loan calculator or the auto loan calculator.

APR Calculator

This APR calculator shows the rate you are really paying once points and fees are counted, not the one on the advertisement. You borrow the full amount and hand part of it straight back at closing, but repay as though you kept all of it. The APR is what makes those two facts consistent.

Example numbers

The answerfrom an example

You are really paying 6.666%, not the 6.500% quoted. The $5,100 of fees is the difference.

Worked on $300,000 at 6.50% over 30 years, 1 point and $2,100 of fees. Change anything below to use yours.

True APR: 6.666%
Note rate: 6.500%
The fees are worth: 0.166% of rate

The figures behind it

True APR: 6.666%; The rate that makes your payments worth exactly the cash you actually received.
Note rate: 6.500%; What the lender quotes for the borrowing alone.
The fees are worth: 0.166% of rate; How far the fees push the APR above the note rate.
Fees paid at closing: $5,100; Points, origination and other charges, deducted from the $300,000 you borrow.
Cash you actually receive: $294,900; The loan less the fees, but you repay as though you had the whole amount.
Monthly payment: $1,896.20; Priced on the full loan amount at the note rate.

What the borrowing costs in total$387,732

99%

Interest over the term$382,632
Discount points1.000% of the loan, paid at closing.$3,000
Origination fee$1,200
Other fees$900

Payment scheduleShow

The table scrolls sideways

Item	Amount
Loan amount	$300,000
Discount points	$3,000
Origination fee	$1,200
Other financed fees	$900
Cash received	$294,900
Monthly payment	$1,896.20
Payments made	360
Total interest	$382,632
Total cost of credit	$387,732
Note rate	6.500%
True APR	6.666%

What this result assumes

The APR is found by solving for the rate at which your payment stream is worth exactly the cash you received, the loan less the fees. That is the definition the Truth in Lending Act uses, and it is why the APR exists as a separate figure from the note rate.
Fees are assumed to be paid at closing out of the loan proceeds. If you pay them separately in cash the arithmetic is the same: the money left your hands either way.
The same fee raises the APR much more on a short loan than a long one, because there are fewer payments to spread it across. That is why paying points suits someone who will keep the loan, and rarely suits someone who will not.
Only fees that are part of the finance charge belong here. Third-party costs a lender does not require, a home inspection you chose, prepaid escrow, title insurance in some states, are excluded from a lender’s official APR, so this figure can differ from a Loan Estimate if you include them.

Methodology

Reviewed September 1, 2026

Two rates, and why they differ

A lender quotes two numbers that sound interchangeable and are not. The note rate prices the borrowing: it is what generates your monthly payment. The APR prices the whole transaction, folding in what it cost you to obtain the loan — discount points, origination, and any other charge deducted from the proceeds.

The mechanism is simple once seen. You borrow $300,000 and hand $5,100 straight back at closing, so $294,900 actually reaches you. But your payment was calculated on the full $300,000. You are therefore paying for money you never had, and the APR is the single rate at which that payment stream is worth exactly the cash you received.

This is the definition the Truth in Lending Act requires lenders to disclose, and it exists precisely because a quoted rate can be bought down with points until it looks better than a competitor that charges none.

How it is solved

There is no closed form for the APR — it is the root of a polynomial in the discount rate — so it is found by bisection. The present value of the payment stream, A × (1 − (1 + r)⁻ⁿ) ÷ r, is evaluated against the net proceeds, and the interval is halved until it is narrower than a twentieth of a basis point.

Present value falls as the discount rate rises, so the difference is monotonic and a single crossing is guaranteed. The test suite pins the defining identity: with no fees at all, the APR must equal the note rate exactly, because the proceeds are then the loan.

The solver is bracketed between 0% and 100%, which covers any consumer loan. A loan whose fees exceed the amount borrowed has no meaningful APR, and the calculator says so rather than returning a number.

Term length changes everything about a fee

The same dollar of fee is recovered across every payment you make, so a fee on a five-year loan bites far harder than the same fee on a thirty-year one. On the default figures, moving the term from 360 months to 60 roughly quadruples the gap between the note rate and the APR without changing a single fee.

This is the practical reason discount points suit some borrowers and not others. Points are a fee paid now to lower the rate later, and "later" has to be long enough to recover it. If you expect to sell or refinance within a few years, the APR is the number that exposes that — the advertised rate will not.

It also means comparing two offers on APR alone is only fair when the terms match. A 15-year loan and a 30-year loan with identical fees will show different APRs for reasons that have nothing to do with which is the better deal.

Assumptions

All fees are paid at closing, out of the loan proceeds.
The payment is level for the whole term and every payment is made on time.
The note rate is fixed. An adjustable-rate loan’s APR depends on rate assumptions this does not make.
The loan runs to full term. Paying it off early raises the effective cost of any up-front fee.
Only fees you enter are included; the calculator cannot know which charges a lender counts in its own finance charge.
Third-party costs a lender does not require — some title and escrow charges, an inspection you chose — are excluded from an official APR and should usually be left out here too.
Mortgage insurance premiums are not included, though a lender’s disclosed APR generally does include them.
Compounding is monthly, matching how US consumer loans are quoted.

Sources

Common questions

What is the difference between APR and interest rate?: The interest rate prices the borrowing and produces your monthly payment. The APR prices the whole deal, adding the fees you paid to get the loan and expressing them as extra rate. If a loan has no fees the two are identical; the bigger the fees, the wider the gap, and the gap is what the advertised rate hides.
How is APR calculated?: By solving for the rate at which your payment stream is worth exactly the cash you received, the loan amount less any fees deducted at closing. There is no formula to rearrange, so it is found numerically. This calculator halves the interval until the answer is accurate to a twentieth of a basis point.
Should I pay discount points?: Only if you will keep the loan long enough to recover them. Points are a fee now for a lower rate later, and the calculator shows the effect directly: shorten the term and watch the APR climb while the fees stay the same. If you expect to move or refinance within a few years, points rarely pay for themselves.
Is the lowest APR always the best loan?: Not automatically. APR assumes you keep the loan for its full term, so it flatters a loan with heavy up-front fees if you plan to leave early. It also only compares fairly across identical terms. Use it to see through advertised rates, then check the total cost of credit, shown above, against how long you actually expect to hold the loan.
Why does my Loan Estimate show a different APR?: Because lenders include a specific set of charges in the finance charge and exclude others. Third-party costs the lender does not require, and prepaid escrow, are generally left out; mortgage insurance is generally put in. Enter only the lender-required fees here and the figures should converge.
Does this work for a car loan or personal loan?: Yes, the arithmetic is identical for any level-payment loan with fees taken from the proceeds. Note that short terms magnify the effect of a fee, so a $500 fee on a three-year personal loan moves the APR far more than the same fee on a mortgage. For the payment itself, use the loan calculator or the auto loan calculator.

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