APR Calculator
✦ Finance & MoneyUse this APR calculator to find the fee-inclusive TILA annual percentage rate on any loan or mortgage — enter your note rate, loan amount and lender fees to get the result, or run it in reverse to see what fees a given APR implies.
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- ✓ Formula and sources shown
The formula
TILA APR — actuarial method (Regulation Z Appendix J)
Net proceeds = PMT x [1 - (1 + APR/12)^(-n)] / (APR/12)
Solved numerically for APR using Newton-Raphson.
Net proceeds = Loan amount - Finance charges
PMT = Loan amount x [(r/12)(1+r/12)^n] / [(1+r/12)^n - 1]APR/12 is the periodic rate; n is the number of monthly payments; PMT is the level monthly payment computed at the note rate on the full loan amount; finance charges reduce the net proceeds. Solver tolerance: 1 x 10^-7 on the periodic rate, exceeding the Reg Z minimum. Payment rounded to the nearest cent. Actuarial method, monthly periods; ARM and balloon loans are out of scope.
Calculating it by hand
- Enter the loan amount — the principal you are borrowing, not the purchase price.
- Enter the annual note rate from your loan contract or Good Faith Estimate.
- Select the loan term in years.
- Enter the origination fee as a percentage of the loan amount (check your Loan Estimate, Box A).
- Enter discount points you are paying (each point = 1% of the loan amount).
- Open "Advanced" to add other lender finance charges (underwriting, processing) or a flat origination fee.
- Read the TILA APR in the results panel — it is higher than the note rate by the fee load. Switch to "APR → Fees" mode to work backwards from a lender's quoted APR to the implied total charges.
Worked examples
$250,000 mortgage at 7%, 30 years, with a 1% origination fee and $1,000 in lender fees
Loan amount: $250,000. Note rate: 7.000%. Term: 30 years (360 payments).Origination fee: 1.000% × $250,000 = $2,500.Other lender fees: $1,000. Total finance charges: $3,500.Net proceeds: $250,000 − $3,500 = $246,500.Monthly payment at note rate on full loan: PMT(7%/12, 360, $250,000) ≈ $1,663.26.Solve: $246,500 = $1,663.26 × [1 − (1 + r_m)^−360] / r_m.Newton-Raphson converges: r_m = 0.005950 per month → annual APR = 7.140%.
TILA APR: 7.140%. The 0.140 percentage-point gap (14 basis points) represents the $3,500 in Reg Z finance charges spread over the 30-year payment stream.
$200,000 loan at 6%, 30 years, zero fees
Loan amount: $200,000. Note rate: 6.000%. Term: 30 years.No origination fee, no points, no other lender fees.Finance charges: $0. Net proceeds = $200,000.When net proceeds = loan amount, the present-value equation reduces to the standard PMT formula at the note rate.APR = note rate: 6.000%.
TILA APR: 6.000% — exactly equal to the note rate when there are no finance charges.
Reverse mode: what fees does a 7.5% APR imply on a $200,000 loan at 7%?
Loan amount: $200,000. Note rate: 7.000%. Term: 30 years. Target APR: 7.500%.Monthly payment at note rate: PMT(7%/12, 360, 200000) = $1,330.60.Net proceeds from APR: PV(7.5%/12, 360, 1330.60) = $190,299.25.Implied finance charges: $200,000 − $190,299.25 = $9,700.75.
Implied finance charges: $9,700.75 — a lender quoting a 7.500% APR on a 7% note-rate, 30-year $200,000 loan is charging about $9,700 in total Reg Z finance charges.
Methodology
What APR actually measures (and what it doesn't)
The APR on a loan is not the same as the interest rate — and it is not the same as APY on a savings account. Those two confusions are the most common mistakes when comparing loan offers, and this page resolves both.
Read sources and limitsHow is the TILA APR calculated?
The federal Truth in Lending Act (TILA) requires every lender to disclose a single Annual Percentage Rate that captures both the interest rate and the prepaid finance charges. On a $250,000, 30-year loan at 7% with $3,500 of finance charges, that rate is 7.140% — the figure this calculator solves for.
The method is defined in 12 CFR §1026.22 and Appendix J to Regulation Z: find the annual rate at which the present value of all scheduled payments equals the net proceeds — the amount the borrower actually receives after the lender deducts the finance charges.
In plain terms: if you borrow $250,000 but pay $2,500 in origination fees and $1,000 in lender processing fees, you receive $246,500 in net proceeds. The APR is the rate that makes the present value of your 360 monthly payments equal exactly $246,500, not $250,000. Because you are receiving less money but making the same payments, the effective cost of the loan is higher than the note rate — and the APR captures that extra cost.
This calculation requires a numerical solver (Newton-Raphson with a bisection fallback), because the equation cannot be solved in closed form for the rate. The solver iterates until the present value is within 1 × 10⁻⁷ of the net proceeds, which exceeds the Regulation Z tolerance of one-half unit in the sixth decimal place of the annual rate.
What counts as a finance charge under Regulation Z?
The APR is only as accurate as the finance charges you include. Regulation Z §1026.4 defines a finance charge as any charge imposed by the creditor as a condition of the loan. The most common finance charges are: origination fees, discount points, underwriting fees, processing fees, mandatory mortgage insurance premiums, and mortgage broker fees.
These all reduce your net proceeds and raise the APR above the note rate.
The charges that do NOT count are third-party closing costs that the borrower would pay regardless of which lender they chose: appraisal fees, credit report fees, title insurance, title search, settlement agent fees, recording fees, transfer taxes, survey fees, and flood determination fees. Including these in the finance-charge total overstates the APR; excluding lender-imposed charges understates it. The checklist in the results panel identifies each category based on the current Regulation Z text.
A practical starting point: look at your Loan Estimate (LE) under TRID. Box A ("Origination Charges") is almost always a finance charge. Box B ("Services You Cannot Shop For") contains a mix — the appraisal is not a finance charge; a mandatory lender fee is. Box C ("Services You Can Shop For") is generally third-party and not a finance charge. Boxes E, F and G (taxes, prepaids, escrow) are not finance charges.
What does the gap between APR and the interest rate tell you?
The gap between the APR and the note rate is a compressed signal for the fee load. A gap of 5-10 basis points (e.g., 7.000% note rate, 7.050% APR) means low fees relative to the loan size — this is typical of a large jumbo mortgage with minimal origination costs.
A gap of 50-100 basis points (e.g., 7.000% vs 7.600%) signals substantial upfront charges.
Because the APR spreads the one-time fees over the life of the loan, the gap shrinks as the term lengthens and grows as the term shortens. On a 5-year loan with the same fee amount, the APR premium is dramatically larger than on a 30-year loan. This is why comparing APRs across loans with different terms can be misleading: a 15-year loan with a higher APR than a 30-year loan is not necessarily more expensive over the period you actually hold it.
The most reliable use of the APR is to compare two loans of the same type and term from different lenders. Two lenders quoting 7.000% at 30 years? The one with the higher APR is charging more in fees. That comparison is the reason Regulation Z requires APR disclosure — use it for that purpose and be cautious about cross-term comparisons.
Is APR the same as APY?
Lenders use "APR" for the fee-inclusive TILA rate; banks and credit card issuers also use "APR" for the nominal rate before compounding. These are genuinely different numbers computed from different formulas, and the confusion between them is extremely common — APY adds compounding, while the loan APR adds fees.
The TILA APR on a loan is not a compounding rate. It is a rate that equates a payment stream to a principal amount — a present-value calculation. In contrast, APY (Annual Percentage Yield) on a savings account, also called EAR (Effective Annual Rate), is the compound growth rate: APY = (1 + r/n)^n - 1. If you deposit money at a 5% APR compounding monthly, your actual annual return is 5.116% APY. Lenders do not compound the TILA APR on your loan balance.
The practical rule: when you are comparing two loan offers, use the TILA APR (this calculator). When you are comparing a savings account, a certificate of deposit, or the effective cost of a credit card, use the EAR/APY (our Effective Annual Rate calculator handles that calculation). The two are numerically different even when the underlying rate is the same.
APR questions
What is APR on a loan?
APR (Annual Percentage Rate) on a loan is the fee-inclusive cost of borrowing expressed as an annual rate, as defined by the federal Truth in Lending Act. Unlike the note rate (the contract interest rate), the APR folds in the prepaid finance charges — origination fees, points, and mandatory lender fees — so you can compare the true cost of two loan offers on an apples-to-apples basis. A 7.000% note rate with $5,000 in fees on a $200,000 30-year loan works out to an APR of roughly 7.250%.
How is APR calculated?
The TILA APR is computed using the actuarial method in Regulation Z Appendix J. The lender subtracts all finance charges from the loan amount to get the net proceeds. The APR is then the annual rate at which the present value of all scheduled monthly payments equals those net proceeds. Because the equation cannot be solved algebraically for the rate, lenders and calculators use an iterative numerical solver (Newton-Raphson is the standard). The result is disclosed on the Loan Estimate and Closing Disclosure under TRID.
What fees are included in APR?
Regulation Z §1026.4 defines finance charges as fees imposed by the creditor as a condition of the loan. These include: origination fees, discount points, underwriting fees, processing fees (when charged by the lender), mandatory mortgage insurance premiums, and mortgage broker fees. They do NOT include third-party fees the borrower would pay regardless of lender: appraisal, credit report, title insurance, title search, settlement agent, recording, transfer taxes, survey, flood determination, or home inspection fees. The distinction matters because including non-finance-charge fees overstates the APR.
What is the difference between APR and interest rate?
The interest rate (note rate) is the rate applied to your outstanding loan balance each month to compute the interest portion of your payment. The APR is a broader cost measure that includes the note rate plus the upfront finance charges, spread over the life of the loan. A lender with a lower note rate but higher fees can end up with a higher APR than a lender quoting a slightly higher rate with minimal fees. For a same-type, same-term comparison, the APR is the number to compare. The interest rate is what determines your monthly payment amount.
What is the difference between APR and APY?
On loans, APR is the TILA fee-inclusive cost rate defined by Regulation Z — it is not a compounding rate. APY (Annual Percentage Yield), also called EAR (Effective Annual Rate), is the compounding equivalent of a nominal rate: APY = (1 + r/n)^n - 1. Banks use this for savings accounts and CDs. The two formulas are unrelated: a 7% TILA APR on a mortgage is computed from a present-value equation; a 7% APY on a CD means money grows at (1.07 - 1) = 7% per year with annual compounding. Never compare a loan APR to a savings APY directly — use our Effective Annual Rate calculator for the compounding question.
Is a lower APR always better?
A lower APR means a lower all-in cost over the life of the loan — if you hold the loan to maturity. But APR spreads one-time fees over the full term, so a loan with a slightly higher APR but lower fees can actually cost less if you sell or refinance before the break-even point. For example, a 0-point loan at 7.1% APR versus a 1-point buy-down at 6.9% APR: the lower-APR loan may cost you more in the first 5 years if you do not hold it 30. Use the break-even concept: months to recoup the fee difference from the payment saving. Our Refinance Calculator handles this comparison.
What is a good APR for a mortgage?
There is no single answer — a good APR depends on market rates, your credit score, loan-to-value ratio, loan type, and the fee structure. What you can control is comparing APRs across lenders for the same loan type and term: the same 30-year conventional loan at the same loan amount. Get at least three Loan Estimates within a short window (rate-shopping within 14-45 days is treated as a single inquiry by credit scoring models). Freddie Mac publishes average weekly rates at freddiemac.com/pmms for context; this calculator does not offer or recommend rates.
How does APR change with loan term?
APR is sensitive to loan term because one-time fees are spread over more or fewer payments. The same dollar amount of fees on a 15-year loan produces a much higher APR premium than on a 30-year loan, because the cost is amortised over half as many payments. Conversely, on a very short loan (5-7 years), even modest fees can create a large APR gap. This is why you should only compare APRs between loans of the same term — a 15-year loan with a lower APR than a 30-year is not necessarily cheaper per year; the APR calculation is built for same-term comparison.
Source notes
Method, sources & limitations
Every figure on this page comes from the formula above applied to the values you enter. Nothing is estimated from market data, and no result is a forecast. These are the sources behind the method and any fixed figures it uses:
- CFPB — Regulation Z §1026.22 (APR computation)
- CFPB — Regulation Z Appendix J (APR computation methods)
- CFPB — Finance charges §1026.4
- CFPB — What is the difference between a mortgage interest rate and an APR?
- CFPB — Loan Estimate (TRID) explainer
Educational information only. Results are estimates produced from the assumptions you enter, and are not financial, tax, legal or medical advice. Check anything that matters against a qualified professional and the cited sources.