APR Calculator,
the true cost your lender hides in fees.

Field guide

APR vs. interest rate: what the difference actually means.

Every loan comes with two numbers: a stated interest rate and an Annual Percentage Rate (APR). They are not the same thing, and the gap between them is the most concise measure of how much a lender is charging you beyond the cost of borrowing the principal.

The interest rate (also called the note rate or nominal rate) tells you the cost of the money itself: the percentage by which your balance grows each year, before compounding. The APR includes that rate plus all mandatory upfront financing costs: origination fees, discount points, application fees, and other lender charges and expresses them as a single annualised figure. Under the federal Truth in Lending Act (TILA), lenders are legally required to disclose the APR whenever they advertise a rate, precisely so borrowers can compare offers on a like-for-like basis.

How APR is calculated

The APR is the internal rate of return (IRR) of the loan cash flows, viewed from the borrower’s perspective. Concretely:

1. Calculate the monthly payment (PMT) at the stated rate on the full loan amount.
2. Subtract all upfront fees from the loan amount to get the net proceeds, the amount the borrower actually receives.
3. Find the interest rate r that makes the present value of all PMT payments equal to the net proceeds:

Solve for r numerically (bisection works reliably), then annualise: APR = r × 12 × 100. This calculation is what this calculator performs: a precise numerical solve, not a simple approximation.

Why APR is always ≥ the interest rate

Because upfront fees reduce the net proceeds without reducing the monthly payment, every fee dollar inflates the effective rate. You pay a full PMT each month, but you received less money to begin with , so you’re effectively paying interest on money you never had. The more fees relative to the loan size, the larger the gap between the rate and the APR.

The spread is measured in basis points (bps), where 100 bps = 1%. A spread of 25 bps means the APR is 0.25% higher than the nominal rate. On a $300,000 30-year mortgage this is roughly $15,000 in extra lifetime cost. A 100 bps spread would represent $60,000 in extra cost, a number that makes the fee structure very visible once expressed this way.

Discount points: what they are and when they make sense

A discount point is 1% of the loan amount paid upfront to “buy down” the interest rate. One point typically reduces the rate by about 0.125% to 0.25%, depending on the lender and market conditions (the 0.125% convention used here is the industry standard approximation for long-term mortgages).

Buying points is essentially a break-even calculation:

If you plan to keep the loan longer than the break-even period, points save money in aggregate; the cumulative payment savings exceed the upfront cost. If you sell or refinance before break-even, you lose.

• Points make sense when rates are high (larger absolute savings), when you plan a long hold, and when you have cash to spare at closing.
• Points rarely make sense in a rising-refinance environment, for short-term loans, or when the cash would earn more invested elsewhere.
• A break-even under 60 months (5 years) is generally considered favourable for a 30-year mortgage; over 84 months (7 years) is generally not.

What fees are included in APR and which are not

Under TILA, the following costs must be included in the APR:

• Discount points and origination points
• Loan origination fees and underwriting fees
• Mortgage broker fees
• Prepaid interest (the odd days of interest at closing, though this is minor)
• Mandatory mortgage insurance premiums (FHA MIP, PMI in some cases)

These costs are excluded from the APR calculation:

• Title insurance and escrow fees
• Appraisal fees and inspection costs
• Attorney fees
• Recording fees and taxes
• Optional services (home warranty, etc.)

Because lenders differ in what they classify as a finance charge, APR comparisons across lenders are more reliable than exact. Two lenders offering identical loans can show slightly different APRs depending on which fees each classifies as a finance charge.

APR on different loan types

APR behaves differently across loan types because the absolute fee amounts are amortised over different periods:

• 30-year mortgage: Fees are spread over 360 payments; APR typically exceeds rate by only 10–50 bps, even with significant fees.
• 5-year auto loan: Same $2,000 in fees amortised over 60 payments; APR can exceed rate by 100–200 bps.
• Personal loan (2–3 years): Upfront origination fees of 5–8% are common; APR can be 300–800 bps above the stated rate, completely changing the cost picture.
• Credit cards: APR is usually identical to the stated rate because there are no upfront financing charges (though annual fees can complicate this).

Using APR to compare loan offers

When comparing two loan offers, use APR rather than the stated rate , but only when the loans have the same term and you plan to hold them to maturity. If you might refinance in 5 years on a 30-year mortgage, the APR comparison overstates the value of a low-fee high-rate offer (since less of the fee amortisation is recouped).

For the most accurate comparison on loans you might not hold to maturity, calculate the total cost at your expected hold period rather than the full APR. This calculator’s lifetime cost breakdown gives you the raw numbers to do exactly that.

Worked example

A borrower takes a $300,000, 30-year mortgage at 7.000% with: 1 discount point ($3,000), $1,500 origination fee, $500 application fee.

• Monthly payment (at 7.000%): $1,995.91
• Net proceeds: $300,000 − $5,000 = $295,000
• Solve r such that PV($1,995.91, 360, r/12) = $295,000 → monthly r ≈ 0.5867%, APR ≈ 7.204%
• Spread: 7.204% − 7.000% = 20.4 bps
• Break-even on 1 point ($3,000): rate without point = 7.125%, payment = $2,021.04 → savings = $25.13/mo → break-even ≈ 119 months (≈ 10 years)

Disclaimer

This calculator is for educational and comparison purposes only. Actual APR figures on loan disclosures may differ due to different fee classifications, rounding conventions, and prepaid interest calculations. Always verify with your lender’s official Loan Estimate or Truth-in-Lending disclosure.