Audited 26 May 2026·Last updated 27 Jul 2026·8 citations·Tier 1·0 uses

APR Calculator

Free APR calculator. Convert a loan's note rate and upfront fees into the true annual percentage rate disclosed under the Truth in Lending Act.

APR Calculator

The face amount of the loan — the gross principal the lender originates, before any fees are netted out of the disbursement.
$
The contractual interest rate stated on the promissory note, used to calculate the scheduled monthly payment. This is the headline rate the lender quotes.
%
Length of the loan in years. The APR is the rate that, charged on the net cash you actually receive, reproduces the same scheduled payments over this term.
yrs
Sum of all finance charges paid at closing: origination fee, discount points, mortgage broker fees, mortgage insurance premiums, and any other Reg Z prepaid finance charges. Exclude title insurance, appraisal, and recording fees.
$
APR
5.18
The annual percentage rate as defined under Regulation Z. This is the rate that, applied to the net amount financed (loan minus upfront finance charges), reproduces the same monthly payment over the same term — the true annualized cost of credit.
Monthly payment
$1,073.64
Total cost of loan
$190,511.57
Effective fee rate
2.00 %

Background.

An APR calculator converts the two numbers a lender quotes you — the note interest rate and the upfront finance charges — into the single number that lets you honestly compare one loan offer against another: the annual percentage rate. The APR is not a marketing figure. It is a federally-mandated disclosure under the Truth in Lending Act (15 U.S.C. § 1601 et seq.) and Regulation Z (12 C.F.R. Part 1026), and it answers a very specific question — what annual rate, charged on the net cash you actually receive at closing, produces the same stream of monthly payments the lender is going to collect from you? The math is iterative because there is no closed-form solution; this calculator runs the same Newton-Raphson iteration that lender APR-disclosure software uses internally, converging on the APR to four decimal places. Enter the gross loan amount the lender will originate, the note rate from your promissory note, the term in years, and the sum of all upfront finance charges — origination fees, discount points, mortgage broker fees, mortgage insurance premiums, and any other charges that Regulation Z classifies as a prepaid finance charge — and you will get back the APR, the scheduled monthly payment, the total all-in cost of the loan over its full term, and the effective fee rate as a percentage of the loan amount.

The headline-rate-versus-true-cost distinction is the entire reason APR exists. A lender can advertise a 5.00% rate on a $200,000 thirty-year mortgage and bury $4,000 in origination and points at closing; another lender can advertise 5.25% on the same loan with zero upfront fees. The first loan's note rate is 25 basis points lower but its APR works out near 5.17%, which means the second offer at 5.25% is actually the cheaper loan over the full term once you account for the cash you paid at closing. The Consumer Financial Protection Bureau's standardized Loan Estimate form, mandated by the TILA-RESPA Integrated Disclosure rule, forces every U.S. lender to display the APR on page 3 alongside the note rate on page 1 precisely so consumers can run this comparison without doing the math themselves.

The calculator also makes the APR-versus-APY distinction explicit. APY (annual percentage yield) describes how interest compounds upward on a deposit account — savings, certificates of deposit, money market funds — and obeys a different formula entirely (APY = (1 + r/n)^n − 1, where r is the nominal rate and n is the compounding frequency). APY belongs to deposits; APR belongs to loans. They are not interchangeable, and a lender quoting APY on a credit product is either confused or selling something. The APR is also not the same thing as the effective annual rate (EAR), which compounds the APR itself to reflect how interest accumulates on the unpaid balance. For a monthly-compounding loan, EAR = (1 + APR/12)^12 − 1, which lifts a 5.17% APR to about 5.29% EAR — but Regulation Z does not require lenders to disclose EAR, and the APR alone is the legally-mandated comparison metric.

A few honest limits of APR. It assumes you hold the loan to maturity. If you sell the house in year five and pay off a thirty-year mortgage, the upfront fees were amortized over five years not thirty, and your effective cost was much higher than the disclosed APR — the same loan, looked at honestly, was a worse deal than the comparison suggested.

APR also does not capture prepayment penalties, balloon payments, adjustable-rate features after the initial fixed period, or the discount-point trade-off where you pay more cash upfront to buy down the note rate. For ARMs, lenders disclose a fully-indexed APR assuming current index values, which can swing materially over the life of the loan. Use this calculator as the right first comparison between fixed-rate offers; for ARM and balloon structures, also compare worst-case payment scenarios.

What is apr calculator?

The annual percentage rate (APR) is a standardized measure of the cost of credit, expressed as a yearly rate, that includes both the periodic interest charged on the loan and the upfront finance charges paid at closing. It was created by the Truth in Lending Act of 1968 and is governed today by Regulation Z, 12 C.F.R. Part 1026, which the Consumer Financial Protection Bureau enforces. The APR is mathematically defined as the rate that, when applied to the net amount the borrower actually receives at closing (the loan amount minus the prepaid finance charges), discounts the future stream of scheduled loan payments back to that net amount. In equation form, it is the rate r that satisfies Net Proceeds = Σ Payment_t / (1 + r/12)^t for t = 1 to n monthly periods. Because there is no algebraic solution for r, every modern APR disclosure is generated by numerical iteration — Newton-Raphson, secant method, or bisection — converging on the rate to four-decimal precision. Regulation Z is explicit about which closing costs qualify as prepaid finance charges that enter the APR calculation: loan origination fees, discount points, mortgage broker fees, mortgage insurance premiums (private MI on conventional loans and the FHA up-front MIP), prepaid interest from closing to the first payment date, and certain third-party fees the lender requires. Costs that do not enter the APR calculation include title insurance, appraisal fees, credit report fees, government recording fees, and homeowners insurance — Regulation Z classifies these as bona fide third-party charges rather than finance charges. The APR's purpose is comparative: it normalizes loan offers with different fee structures so the borrower can rank them by true cost, which is why every consumer credit disclosure since 1968 has been required to display it with equal prominence to the note rate.

How to use this calculator.

  1. Enter the gross loan amount the lender will originate. This is the face value on the promissory note, not the cash you will actually receive at closing if origination fees are netted out.
  2. Enter the note interest rate from your loan agreement or Loan Estimate page 1. This is the rate used to calculate the contractual monthly payment — never the APR itself.
  3. Enter the term in years. Thirty for a standard mortgage, fifteen for a fast-payoff mortgage, five to seven for most auto loans, two to seven for unsecured personal loans.
  4. Enter the total upfront finance charges. On a Loan Estimate this is the sum of origination charges (page 2 section A), discount points if any, mortgage insurance premiums financed at closing, and any lender or broker fees Regulation Z classifies as prepaid finance charges. Exclude title insurance, appraisal, credit report, and recording fees.
  5. Read the APR — the headline output. Compare it directly to the APR on any competing loan offer over the same term. The lower APR is the cheaper loan if you hold it to maturity.
  6. Use the effective fee rate as a sanity check. Heavy upfront fees on a short loan inflate the APR sharply (a $4,000 fee on a five-year loan adds far more APR than the same fee spread over thirty years), which is why APR alone can mislead when you plan to refinance or sell early.

The formula.

P − F = M × [ 1 − (1+i⁄12)⁻ⁿ ] ⁄ (i⁄12)
P · loan amountF · upfront finance chargesM · monthly paymenti · APR (solved iteratively)n · # of payments

The note-rate monthly payment is calculated first using the standard amortizing-loan formula M = P × [r(1+r)^n] / [(1+r)^n − 1], where P is the gross loan amount, r is the periodic monthly note rate (annual rate ÷ 100 ÷ 12), and n is the total number of monthly payments (term in years × 12). The APR is then solved as the rate i that satisfies (P − F) = M × [1 − (1 + i/12)^(−n)] / (i/12), where F is the upfront finance charges. There is no algebraic solution; the calculator uses Newton-Raphson iteration starting from the note rate as the initial guess, evaluating the present-value function and its analytic derivative each iteration, terminating when successive estimates differ by less than 1e-8. Convergence is reliable for any realistic loan because the function is monotonically decreasing in i. Total cost of loan is M × n + F. Effective fee rate is F / P expressed as a percentage — useful for comparing the fee load across offers before running the full APR math.

A worked example.

Example

Take a $200,000 thirty-year mortgage at a 5.00% note rate with $4,000 in upfront origination fees and discount points — a realistic 2026 conforming-loan profile. The contractual monthly payment lands at $1,073.64, computed against the full $200,000 principal at the 5.00% rate. Over 360 payments the lender collects $386,511.57 in scheduled payments, and you have already handed over $4,000 at closing, so the all-in total cost of the loan is $390,511.57. The APR works out to roughly 5.17% — seventeen basis points above the note rate — because the calculator solves for the rate that, applied to the $196,000 you actually netted at closing, produces those same $1,073.64 monthly payments over thirty years. A competing lender quoting 5.25% with zero upfront fees would have an APR of exactly 5.25%, which means the second offer is the cheaper loan over the full thirty-year term despite carrying a higher headline rate. The effective fee rate of 2.00% on this loan is the sanity check — if those same $4,000 in fees sat on a five-year personal loan instead, the effective fee rate would still be 2.00% but the APR impact would be roughly five times larger because the fees would amortize over sixty payments instead of three hundred and sixty.

upfront Fees4,000
annual Rate5
loan Amount200,000
term Years30

Frequently asked questions.

What is the difference between APR and the note interest rate on a loan?
The note interest rate (also called the nominal rate or contract rate) is the percentage stated on your promissory note and used to calculate the scheduled monthly payment against the full loan balance. The APR is a separate, federally-mandated disclosure under the Truth in Lending Act that bundles the note rate together with the upfront finance charges paid at closing — origination, discount points, mortgage broker fees, mortgage insurance — and re-expresses them as a single annualized rate against the net cash you actually receive. The APR is always equal to or higher than the note rate. The Consumer Financial Protection Bureau requires the APR to appear on page 3 of every Loan Estimate alongside the note rate on page 1 precisely so consumers can compare offers by true cost rather than by headline rate. Always shop loans by APR; pay your bills by the note rate.
Why is APR the only honest way to compare loan offers?
Because lenders compete on two surfaces at once — the headline interest rate and the closing-cost structure — and they can shift cost between the two without changing the all-in price. A lender can advertise an artificially low note rate and recoup the spread by charging more discount points at closing; another can offer a higher rate with no points and still win on lifetime cost. The note rate alone tells you nothing about which loan is cheaper. APR collapses both dimensions into a single number by asking what rate, applied to the cash you actually net at closing, reproduces the same payment stream. Two loans with the same APR are the same loan in economic terms, regardless of how the closing-day cash flows differ. That is exactly why Regulation Z requires APR disclosure with equal prominence to the note rate — it is the only metric that prevents the rate-versus-fees shell game from misleading borrowers.
What fees are included in the APR calculation and which are excluded?
Regulation Z, 12 C.F.R. Part 1026.4, defines a 'finance charge' as the cost of credit as a dollar amount. Fees that count toward APR include loan origination fees, discount points, mortgage broker fees, private mortgage insurance premiums, the FHA up-front mortgage insurance premium, prepaid interest from closing to the first payment date, and any other lender or required-third-party charges that the lender imposes as a condition of the credit. Fees that do not count toward APR (because Regulation Z classifies them as bona fide third-party charges rather than finance charges) include title insurance, appraisal fees, credit report fees, government recording and transfer fees, homeowners insurance, and inspection fees. The line between included and excluded fees is sometimes contested at the margins — a fee the lender requires for its own benefit is generally a finance charge, while a fee the borrower would pay regardless of how the property was financed is generally not.
What is the difference between APR and APY?
APR (annual percentage rate) is a borrowing disclosure governed by the Truth in Lending Act — it expresses the cost of credit on a loan as a simple annualized rate that incorporates upfront fees but does not compound. APY (annual percentage yield) is a saving disclosure governed by the Truth in Savings Act — it expresses the earning rate on a deposit account as a compounded annualized rate, calculated as APY = (1 + r/n)^n − 1 where r is the nominal rate and n is the compounding frequency. APR belongs to debts; APY belongs to deposits. They are not interchangeable. A 5% APR loan compounded monthly costs you an effective annual rate of about 5.12% — but Regulation Z does not require that compounded figure to be disclosed, and lenders never quote it. If a lender ever uses 'APY' to describe a loan rate, treat it as either an error or a deliberate attempt to make the loan look cheaper than it is.
How is APR calculated mathematically?
The APR is the rate i that satisfies (Loan Amount − Upfront Finance Charges) = Σ Monthly Payment / (1 + i/12)^t, summed over t = 1 to n months. The scheduled monthly payment is computed first from the note rate using the standard amortizing-loan formula M = P × [r(1+r)^n] / [(1+r)^n − 1]. Because there is no closed-form algebraic solution for the APR equation, lenders and this calculator use numerical iteration — typically Newton-Raphson — starting from the note rate as the initial estimate and converging on the APR to four decimal places. Regulation Z Appendix J specifies the acceptable mathematical methods and provides reference test cases that disclosure software must match within a tolerance of one-eighth of one percentage point. The numerical convergence is fast and reliable because the present-value function is monotonically decreasing in the discount rate.
Does APR account for prepayment penalties or early payoff?
No, and this is one of APR's most important limits. The APR assumes you hold the loan to its stated maturity. If you refinance, sell the property, or otherwise pay off the loan early, the upfront finance charges were amortized over a much shorter period than the APR calculation assumed, which means your effective cost of credit was materially higher than the disclosed APR. On a thirty-year mortgage with $4,000 in upfront fees, holding to maturity gives you a 5.17% APR; selling after five years on the same loan gives you an effective cost closer to 5.50%. Prepayment penalties (where the lender charges a fee to pay the loan off early) are also excluded from the APR figure, even though they are very much a real cost. Always read your loan documents for prepayment terms separately, and run a break-even analysis on any decision that involves paying upfront points to buy down the note rate.
Why does adding upfront fees make a short loan's APR jump much more than a long loan's?
Because the same dollar amount of fees gets amortized over a different number of payments. A $4,000 upfront fee on a thirty-year mortgage spreads across 360 monthly payments; on a five-year auto loan, it spreads across 60. The shorter loan absorbs roughly six times the APR impact per dollar of fee, because the math is essentially asking how much extra annualized rate is needed to make the lender whole on $4,000 of foregone principal over either thirty years or five. On a $200,000 thirty-year loan at a 5% note rate, $4,000 in fees adds about 17 basis points of APR. On a $25,000 five-year loan at the same note rate, $4,000 in fees adds nearly 350 basis points of APR — turning a headline 5% loan into an effective 8.5%. This is why upfront fees matter much more on short loans, and why borrowers should be especially skeptical of origination fees on personal loans and auto loans.
Is APR the same as the effective annual rate (EAR)?
No. The APR is a simple annualized rate that does not compound — it multiplies the periodic rate by the number of periods per year. The effective annual rate (also called the effective interest rate) accounts for compounding within the year, calculated as EAR = (1 + APR/m)^m − 1, where m is the compounding frequency. For a monthly-compounding 5.17% APR loan, the EAR works out to about 5.29%. EAR is the more economically accurate measure of borrowing cost because it captures how interest actually accumulates on the unpaid balance, but Regulation Z does not require EAR disclosure on consumer loans — only APR. The gap between APR and EAR widens at higher rates and shorter compounding periods, which is why credit-card disclosures can show a very different effective cost than the stated APR suggests when you carry a balance with daily compounding.
How does APR work for adjustable-rate mortgages (ARMs)?
For an ARM, Regulation Z requires lenders to disclose a fully-indexed APR that assumes the index rate at the time of disclosure remains constant for the life of the loan. In practice, the index moves, so the actual APR you pay over thirty years on a 7/1 ARM almost certainly will not equal the disclosed APR. Lenders must also disclose the worst-case scenario — the maximum rate the loan could reach under its rate caps and how that would change the payment. Comparing ARMs by APR alone is unreliable because two ARMs with the same initial APR can have very different rate-cap structures and index margins. For ARM comparisons, look at the initial fixed-period APR, the index margin, the periodic rate caps, the lifetime cap, and run a worst-case payment scenario alongside the APR figure. This calculator models fixed-rate loans and is the right tool for fixed-rate APR comparisons; use a dedicated ARM calculator for adjustable products.
Where does the Truth in Lending Act mandate APR disclosure, and what happens if a lender gets it wrong?
The Truth in Lending Act (15 U.S.C. § 1601 et seq.), enacted in 1968 and now implemented by Regulation Z (12 C.F.R. Part 1026) under the Consumer Financial Protection Bureau, requires every creditor extending consumer credit to disclose the APR with the same prominence as the note rate. For closed-end loans, the APR appears on the Loan Estimate (TRID disclosure, page 3) and the Closing Disclosure. The accuracy tolerance under Regulation Z is one-eighth of one percentage point for regular transactions and one-fourth of one percentage point for irregular transactions; APRs disclosed outside that tolerance trigger a violation. Remedies include borrower-elected rescission rights (within three years for material disclosure errors on a refinance secured by the principal dwelling), statutory damages, attorney's fees, and CFPB enforcement action. The disclosure regime exists precisely because the APR is a non-trivial calculation — without it, comparison shopping for credit would be functionally impossible for ordinary consumers.

References& sources.

  1. [1]Consumer Financial Protection Bureau — What is the difference between a mortgage interest rate and an APR? (official explainer of APR vs note rate)
  2. [2]Consumer Financial Protection Bureau — Loan Estimate explainer (TILA-RESPA Integrated Disclosure, where APR is mandated to appear on page 3)
  3. [3]Federal Reserve / Code of Federal Regulations — Regulation Z, 12 C.F.R. Part 1026 (full Truth in Lending implementing regulation, including § 1026.4 finance charge definition and Appendix J APR calculation method)
  4. [4]Truth in Lending Act — 15 U.S.C. § 1601 et seq. (statutory basis for APR disclosure)
  5. [5]IRS Publication 936 (2025) — Home Mortgage Interest Deduction (clarifies which mortgage interest is deductible; relevant when assessing after-tax effective cost vs APR)
  6. [6]Federal Trade Commission — Truth in Lending Act overview and consumer rights
  7. [7]Bankrate — APR vs interest rate methodology and worked examples
  8. [8]Consumer Financial Protection Bureau — Compliance Guide to Regulation Z (operational guidance for lenders on calculating and disclosing APR)
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