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Mortgage & Loans
APR Calculator — True Annual Cost of a Loan With Fees & Points
The number that tells you what a mortgage or loan really costs once fees are in
When you shop for a mortgage, auto loan or personal loan, the lender quotes you two numbers that look almost the same but mean very different things: the interest rate and the APR (Annual Percentage Rate). The interest rate prices only the loan balance you carry month to month. The APR is the cost of borrowing plus the upfront fees — origination charges, discount points, processing and underwriting fees — spread back across the life of the loan and expressed as one yearly percentage. That's why federal Truth-in-Lending rules make lenders show both: the APR is the honest, apples-to-apples number for comparing offers.
Here's the key idea. You borrow $200,000, but the lender charges $5,000 in fees, so you really only receive $195,000 of usable money — yet your monthly payment is still calculated on the full $200,000 at the quoted rate. Because you're paying back a $200,000 schedule on $195,000 of cash, your effective cost is higher than the sticker rate. The APR is the single rate that, applied to the money you actually pocketed, reproduces that exact payment stream.
The math runs in two steps. First, the standard amortized monthly payment:
Payment = P × r ÷ (1 − (1 + r)⁻ⁿ)
where P is the loan amount, r is the monthly interest rate (annual rate ÷ 12), and n is the number of months. For $200,000 at 6% over 360 months: r = 0.005, so Payment = 200,000 × 0.005 ÷ (1 − 1.005⁻³⁶⁰) ≈ $1,199.10/month.
Second, you solve for the APR. You keep that same $1,199.10 payment and the same 360 months, but ask: what monthly rate makes the present value of those payments equal $195,000 — the net cash you received? There's no clean algebra for this, so the calculator solves it numerically (it tries rates until the present value lands on $195,000). The answer here is about 6.23% APR — higher than the 6% nominal rate, and that gap is the price of the fees.
A quick rule of thumb: APR is always higher than the nominal rate when fees exist, and equal to it when there are none. The bigger the fees and the shorter the loan, the wider the gap, because there are fewer years to spread those upfront costs over.
The most common mistake borrowers make is comparing loans by interest rate alone. A 5.75% loan with $8,000 in points can easily cost more than a 6.00% loan with no fees. APR is the number that exposes that — but only when both loans run the same term. Treat these results as estimates: real APR also depends on which fees a lender includes, and that varies by loan type.
📖 See also: Should You Refinance Your Auto Loan?
Calculator
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📰 Formula
• Monthly rate: r = nominal annual rate ÷ 12 • Monthly payment: PMT = P × r / (1 − (1 + r)^−n) • Net amount received: Net = loan amount − fees • APR: find the monthly rate i where Net = PMT × (1 − (1 + i)^−n) / i, then APR = i × 12 • APR > nominal rate whenever fees > 0
📰 Formula
• Monthly rate: r = nominal annual rate ÷ 12 • Monthly payment: PMT = P × r / (1 − (1 + r)^−n) • Net amount received: Net = loan amount − fees • APR: find the monthly rate i where Net = PMT × (1 − (1 + i)^−n) / i, then APR = i × 12 • APR > nominal rate whenever fees > 0
🧪 Worked examples
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Example 2
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Example 3
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Example 4
⚠️ Common mistakes
- Comparing loans by interest rate alone and ignoring the fees — APR is the fair comparison.
- Comparing the APR of a 15-year loan against a 30-year loan (different terms aren't comparable).
- Entering the monthly rate where the annual rate is asked, or mixing up months and years for the term.
- Assuming APR includes everything — some third-party costs may be left out, so it's still an estimate.
💡 Tips
- Only compare APRs when the two loans have the same term length and loan amount.
- The shorter the loan, the bigger the gap between APR and the nominal rate, because fees spread over fewer years.
- If a lender quotes an APR equal to the rate, ask where the fees went — they may be excluded or rolled in differently.
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❓ Frequently asked questions
What is the difference between APR and interest rate?
The interest rate covers only the charge for the loan balance itself. The APR rolls that rate together with upfront fees and discount points into a single yearly percentage, so it reflects the loan's true cost. With zero fees the two numbers match; add fees and the APR climbs above the rate.
Why is my APR higher than my interest rate?
Because the APR folds in fees you pay upfront. You borrow the full amount but receive less after fees, while still repaying on the full balance — so your effective yearly cost is higher than the quoted rate.
Is a lower APR always the better loan?
Usually, if the terms match. A lower APR on the same loan amount and term means a lower true cost. But always confirm the term length is the same — a low APR on a longer loan can still cost more total interest.
Does APR include closing costs on a mortgage?
It includes finance charges like origination fees, discount points and certain lender fees. It typically excludes third-party costs like title insurance, appraisal and recording fees, so treat the APR as an estimate of the financed cost.
What are discount points and how do they affect APR?
Points are upfront fees you pay to lower your interest rate — one point equals 1% of the loan amount. They raise your APR in the short run because they're a cost, but can lower it over the full term if you keep the loan long enough.
How is APR calculated on a loan?
First the monthly payment is found from the loan amount, rate and term. Then the calculator solves for the rate that makes the present value of those payments equal the net amount you received after fees. That rate, times 12, is the APR.
Is APR the same on credit cards as on loans?
The idea is similar — APR is the yearly cost — but credit card APR usually has no upfront fees, so it tracks the interest rate closely. On loans and mortgages, fees and points push the APR above the rate.
Should I pay points to lower my rate?
It depends how long you'll keep the loan. Points raise your APR upfront but lower your monthly payment. If you'll hold the loan past the break-even point (where the payment savings cover the points), it can pay off.
Why do two lenders quote different APRs for the same rate?
Because they charge different fees and may include different costs in the APR. That's exactly why APR matters: it reveals fee differences that the interest rate alone hides.