APR vs Interest Rate Calculator 2026: TILA & Reg Z explained
Calculate the true APR including all TILA-required fees, compare side-by-side with Brazilian CET (CMN Resolution 4.881/2020), detect deceptive advertising, convert APR ↔ APY, and learn the regulatory difference between US and BR transparency rules.
Based on 14 official sources↓APR
MINOR
Advertised rate: 12.00% APR. Calculated APR: 13.77%. Gap of 14.7% (+1.77 percentage points).
Finance charge decomposition
| Interest | US$3,914.44 |
| Origination | US$500.00 |
| Grand total finance charge | US$4,414.44 |
What is NOT in the APR (educational)
- Late payment fees and penalty fees
- Taxes paid to public officials (registration, security interest)
- Premium for insurance in lieu of perfecting security interest
- Charges for unanticipated late payment
- Bona fide and reasonable appraisal fees in real-property transactions
- Title insurance premiums
- Most discount points (when optional)
Deceptive-advertising detector
Small gap typical for prime loans. APR is usually slightly higher than rate due to fees included by TILA.
Applicable regulation: TILA / Reg Z
Official text · Most recent amendment: April 8, 2026
APR is the cost of credit expressed as a yearly rate. Because it measures the TOTAL cost of credit (including finance charges, fees, and credit-guarantee insurance), APR is NOT an interest rate — it is a measure of total cost. Annualized as SIMPLE: APR = 12 × monthly rate (Reg Z Appendix J).
Annualization convention: Simple: APR_annual = 12 × APR_monthly (Reg Z Appendix J — independent of compounding frequency)
What must be disclosed (9)
- Annual Percentage Rate — must be more conspicuous than any other rate
- Finance Charge (total cost of credit)
- Amount Financed
- Total of Payments
- Payment schedule
- Origination fees, application fees (when condition of credit)
- PMI (Private Mortgage Insurance) — when applicable
- Commitment fees paid by consumer
- Service charges tied to the credit
Consumer protections (5)
- Standardized pre-contract disclosures
- 3 business-day right of rescission for principal-dwelling loans (extended to 3 years if disclosures inadequate)
- Private right of action + regulatory enforcement (CFPB)
- APR tolerance ±0.125 pp on mortgages (HOEPA threshold) / $5-10 finance charge tolerance
- CFPB enforcement authority since 2011 (Dodd-Frank Act)
US vs BR regulatory comparison
| Aspect | US (TILA / Reg Z) | Brazil (4.881/2020) |
|---|---|---|
| Statute base | 15 USC §§ 1601 et seq. (1968) | Lei 4.595/1964 |
| Implementing regulation | 12 CFR Part 1026 (Regulation Z) | Resolução CMN 4.881/2020 |
| Most recent amendment | April 8, 2026 | December 23, 2020 |
| Regulator | CFPB (since Dodd-Frank, 2011) | Banco Central / CMN |
| Annualization convention | Simple: APR = 12 × monthly rate (Reg Z Appendix J) | Compound: CET = (1 + i_m)^12 − 1 |
| Includes IOF / loan tax | N/A (rare in US) | YES — mandatory (Art. 3º) |
| Mortgage insurance | YES — PMI included | YES — DFI/MIP included |
| Excludes late fees | YES | YES |
| Applies to rural credit | YES | NO — Art. 9º exclusion |
| Document retention | ~2 years (typical) | 5 years (Art. 7º) |
| Right of rescission | 3 business days (mortgages) | 7 days CDC (door-to-door / online) |
| Federal interest rate cap | No (state usury laws vary) | No (Selic-linked) |
APR is not an interest rate. The Truth in Lending Act (TILA) is explicit on this — Reg Z and CFPB guidance both state that "since an APR measures the total cost of credit, including transaction charges and premiums for credit guarantee insurance, it is not an interest rate as that term is generally used." If your loan has any fees at all, the APR will be higher than the nominal rate. The gap is the actual cost of those fees expressed as an annual rate, calculated by Newton-Raphson IRR over the cash flow.
Brazil has the same problem with a different law. CMN Resolução 4.881/2020 (effective February 1, 2021) defines CET (Custo Efetivo Total) as the rate that consolidates "all charges and expenses of a credit operation as of the calculation date" — interest, IOF, fees, mandatory insurance, third-party service payments. The compounding convention differs from US APR (Brazil annualizes monthly to annual via compound (1+i)^12 − 1, while US Reg Z Appendix J uses simple 12 × monthly), but the Newton-Raphson IRR engine is identical.
This calculator computes both, side-by-side. It detects the gap between advertised rate and the real APR/CET, classifies severity (none/minor/moderate/severe/abusive), benchmarks against published market medians, and converts APR ↔ APY for the savings vs loan distinction. Worked examples were generated by running the calculator itself — numbers in the prose match what you see in the widget.
How APR (TILA / Reg Z) and CET (Resolução 4.881/2020) actually work
APR is the IRR of the actual cash flow. Reg Z Appendix J says: take amount financed (principal − retained fees), then find the rate that makes the present value of payments equal to amount financed. APR = 12 × monthly_rate (simple, not compound). This is independent of compounding frequency, day-count convention, or month length — TILA chose a single arithmetic for all loans so consumers can compare apples to apples.
CET is the same math, compound-annualized. Resolução 4.881/2020 Art. 4º: solve for the rate that satisfies FC0 = Σ FCj / (1+i)^((dj − d0)/365). The difference from US APR is the annualization: BR uses compound (1 + i_monthly)^12 − 1; US uses simple 12 × i_monthly. Same IRR engine, different annualization convention.
What enters: the regulator-defined "finance charge". TILA § 1605 enumerates: interest charges, origination fees, application fees (when condition of credit), PMI, premiums for credit-guarantee insurance, commitment fees paid by the consumer, service charges related to the credit. Resolução 4.881 Art. 3º enumerates: interest, IOF, bank fees (cadastro/admin), mandatory insurance, third-party service payments. The lists overlap mostly — the big BR addition is IOF (taxa nominal + 0.0082%/dia capped 365 days), absent in the US.
What is excluded. TILA excludes: late fees, taxes paid to public officials, premiums for insurance in lieu of perfecting security interest, charges for unanticipated late payment, and (in real-property loans) bona fide and reasonable appraisal/title fees. Resolução 4.881 Art. 9º excludes: rural credit, external-funds passthroughs. Both regimes exclude optional insurance — opting out reduces total cost without affecting the disclosed rate.
Why APR < APY. APY (Truth in Savings Act / Reg DD) is the EFFECTIVE annual rate after compounding: APY = (1 + APR/n)^n − 1. For monthly compounding (n = 12), 12% APR ↔ 12.6825% APY. For daily (n = 365), 10% APR ↔ 10.5156% APY. The gap is the compounding bonus you earn on savings (or pay extra on loans). Banks disclose APY on deposit accounts and APR on credit accounts — by regulatory design, savings highlight effective gain and loans highlight stated cost.
P = Σ Aj / (1 + i)^tj → solve for i → APR = 12 × i (simple, US) or CET = (1+i)^12 − 1 (compound, BR) APY ↔ APR: APY = (1 + APR/n)^n − 1; APR = n × ((1 + APY)^(1/n) − 1)
- P
- Amount financed (principal − retained fees)
- Aj
- Payment at period j (PMT + monthly fees + insurance + PMI)
- i
- Monthly periodic rate solved by Newton-Raphson IRR
- n
- Compounding frequency for APR↔APY (12 monthly, 365 daily)
Practical examples
BR — R$ 10,000 personal loan at 2%/month, 24 months, R$ 200 origination + IOF
Setup: You see an ad for "2% per month" personal loan. R$ 10,000 principal, 24-month term, R$ 200 origination fee retained at disbursement, IOF enabled (0.38% fixed + 0.0082%/day capped at 365 days).
**Advertised rate (annualized):** (1.02)^12 − 1 = **26.82% AA**. **CET:** Newton-Raphson IRR over cash flow = **34.39% AA**. **Gap: +7.56 percentage points (+28.2%)** vs advertised — severity MODERATE. **Decomposition:** interest R$ 2,689 + IOF R$ 337 + origination R$ 200 = R$ 3,226 total finance charge. The CET exceeds 1.5× the BR market benchmark for personal_unsecured (~21.7% AA), so the calculator flags this as ABOVE the abusive threshold — strong signal to comparison-shop.
Takeaway: A 2%/month advertisement compounds to 26.82% annually, but the CET that includes IOF + origination is 34.39%. The compounding convention (CET uses (1+i)^12 − 1) plus the fees stack to a 7.56 percentage-point gap. Resolução 4.881/2020 Art. 8º requires advertisements that mention interest rate to ALSO mention CET — when only the rate is shown, that is a regulatory red flag.
US — $20,000 personal loan at 12% APR, 36 months, $500 origination
Setup: Standard prime-credit personal loan. Bank advertises "12% APR" — but the $500 origination is retained upfront, not added to the loan balance.
**Advertised:** 12% APR (simple annualization, 12 × monthly_rate). **Calculated APR (with origination):** **13.39% APR**. **Gap: +1.39 percentage points (+11.6%)** — severity MINOR (within the typical prime-credit range). The IRR engine solves: $19,500 (net of $500 fee) = Σ payments / (1 + i)^t over 36 months → i ≈ 1.116% monthly → APR = 12 × 1.116 = 13.39%. Reg Z requires this APR be disclosed more conspicuously than any other rate.
Takeaway: A $500 origination on $20,000 over 36 months adds 1.39 percentage points to APR — exactly what TILA was designed to surface. When comparing two lenders both quoting "12%" but with different origination fees, the APR is the only honest comparison. CFPB has taken enforcement action against lenders that under-disclose APR by more than 0.125 pp on mortgages (HOEPA threshold).
US — $300,000 mortgage at 7%, 30 years, $5k closing + PMI $200/mo
Setup: Conventional 30-year mortgage at the Bankrate average 7%. $5,000 closing costs retained at funding. PMI of $200/month (typical for <20% down, removed automatically at 22% equity per HPA 1998).
**Advertised:** 7.00% APR. **Calculated APR with closing + PMI:** **8.07% APR** — gap of 1.07 percentage points. **Decomposition:** interest $418,527 + closing $5,000 + PMI $72,000 = $495,527 finance charge over 30 years. The PMI alone is $72k — but it disappears at month ~84-100 in a typical equity-build path; the calculator shows the worst-case 360-month total. **TILA Right of Rescission:** 3 business days for principal-dwelling loans (extended to 3 years if disclosures inadequate, per 15 USC § 1635).
Takeaway: The PMI is the big-ticket item. If you can avoid it (20% down or eliminating early), you save the equivalent of 1+ percentage point of APR. Compare two lenders at "7% rate" — the one with lower closing costs and faster PMI removal almost always wins on true APR. CFPB enforcement has gone after dealers who hide closing-cost markup or fail to remove PMI on schedule.
BR — Mortgage R$ 300,000, 11% AA, 30 years, sem IOF, com seguro habitacional
Setup: Brazilian property mortgage, 11% annual rate, 30 years, IOF exempt (real-estate financing exception), R$ 80/month mandatory DFI/MIP insurance.
**Advertised:** 11.00% AA. **CET:** **11.39% AA** — gap of only 0.39 percentage points (severity NONE). The mortgage is the most transparent BR credit product — IOF exempt and only mandatory insurance differs between rate and CET. **Decomposition:** interest R$ 686,425 + insurance R$ 28,800 = R$ 715,225 total finance charge over 30 years. With principal R$ 300k, that is R$ 1.05M paid back — typical for 30-year amortization at 11%.
Takeaway: Mortgages have the smallest CET-vs-rate gap in Brazil because IOF is exempt and bank fees are typically negotiated away in this product. If you see an advertised mortgage rate at 11% but the CET shows 13%+, ask for the cálculo CET (Art. 7º — bank must retain for 5 years). DFI/MIP insurance is mandatory by Resolução BCB 4.676/2018 and properly enters CET; some banks try to add optional insurance at signing — those do NOT enter CET and you can refuse.
APR ↔ APY — when 12% is not 12%
Setup: You see a savings account that pays "12% per year" — is that APR or APY? The answer matters for $10,000 in 1 year: APR linear gives $11,200 (12% × $10k); APY compound gives $11,268.25 (monthly compounding) — a $68.25 gap from the same nominal rate.
**12% APR compounded monthly → 12.6825% APY.** Formula: APY = (1 + APR/n)^n − 1 = (1 + 0.12/12)^12 − 1 = 0.126825. **12% APY → 11.39% APR (compounded monthly).** Formula: APR = n × ((1 + APY)^(1/n) − 1). **Daily compounding (n = 365):** 5% APR → 5.13% APY. **Continuous limit:** APY = e^APR − 1 (n → ∞).
Takeaway: APR is "what they charge per period × periods" — simple. APY is "what you actually keep after compounding" — effective. For loans, regulators force disclosure of APR (Reg Z) — easier to compare against other loans. For savings, regulators force disclosure of APY (Reg DD) — shows actual yield. The mismatch is intentional. When in doubt, ask: "is this rate before or after compounding?" If they cannot answer, walk away.
Practical tips — detecting under-disclosure
- BR — request the demonstrativo de cálculo. Resolução 4.881/2020 Art. 7º obliges banks to produce and retain (for 5 years) a calculation worksheet showing every component of CET. If the bank refuses, that is a regulatory violation reportable to BCB. The worksheet must show the complete cash flow plus the IRR computation.
- US — request the Loan Estimate (TRID). Required by TILA-RESPA Integrated Disclosures (TRID) — within 3 business days of application, the lender must provide a 3-page Loan Estimate with APR, finance charge, monthly payment, and closing costs. If you do not get it, the loan is non-compliant.
- Compare APR, not rate. Two lenders quoting the same nominal rate can have wildly different APRs because of fee structure. The whole point of TILA / Resolução 4.881 is that APR/CET is the apples-to-apples comparison.
- Optional insurance never enters CET/APR. If your monthly payment includes an "insurance" line that is not legally mandatory (DFI/MIP for mortgages; group-life for some loans), opting out reduces total cost without affecting the disclosed CET. This is the single highest-leverage decision available.
- For real-property loans US, exercise the Right of Rescission window. TILA § 1635: 3 business days after consummation to rescind a principal-dwelling loan with no penalty. If the lender's disclosures are incomplete or wrong, that window extends to 3 YEARS — which is also why lenders are conservative about disclosure compliance.
- Watch for "0% APR" car offers with cash rebate alternatives. The dealer typically gives you the choice: 0% financing OR a $2,000 cash rebate at signing. The cash rebate is the "true" cost of the 0% — calculate effective APR by treating the foregone rebate as an upfront fee. Often the cash rebate plus a market-rate loan beats the "0%" headline.
- Beware revolving credit (BR) and credit cards (US). BR rotativo: BCB regulates the maximum but CET often exceeds 100% AA. US credit cards: 22.5% APR average, with some sub-prime cards at 30%+. Both products use APY-style compounding daily — actual cost is far higher than the disclosed monthly rate.
Limitations and edge cases
Variable-rate loans (ARM US, IPCA-indexed BR). This calculator assumes a fixed rate for the term. ARM mortgages and IPCA-indexed Brazilian mortgages have rates that change over time — the disclosed APR/CET uses the rate AT CALCULATION DATE per Reg Z and Resolução 4.881 Art. 5º, but actual cost will move.
Reverse mortgages (US TILA § 1026.33). Special disclosure rules apply (HECM-specific). Not modeled here.
State usury laws (US). This calculator uses federal TILA. Some states cap interest rates beyond TILA — Massachusetts, New York, and others. Always check your state if the calculated APR seems extreme.
HOEPA (high-cost) mortgages. Loans above HOEPA thresholds get extra disclosures. Not differentiated here.
Refinance / cash-out refinance. The cash flow modeled is a single new loan; refinancing a previous loan involves payoff statements, prepayment penalties, and other items.
Business loans US (TILA does not apply directly). Most commercial loans are exempt from TILA. Brazilian Resolução 4.881 covers ME/EPP only — larger PJ exempted.
Brazilian credit cards (rotativo). The calculator simplifies revolving credit; Resolução 4.881 Art. 6º specifies a 30-day standard term, but actual revolving balances move daily.
Frequently asked questions
Why is APR not the same as the interest rate?▾
TILA / Reg Z is explicit: APR measures TOTAL cost of credit including fees, origination, PMI, and credit-guarantee insurance. The interest rate is just one component. CFPB guidance: "Since an APR measures the total cost of credit, it is not an interest rate as that term is generally used." If your loan has any fees, APR > rate.
Why is CET (Brazil) higher than the advertised rate?▾
Resolução 4.881/2020 Art. 3º requires CET to include interest + IOF + bank fees + mandatory insurance + third-party service payments. The advertised rate usually shows only the interest. The gap is the IOF (~0.38% + daily) plus origination plus admin fees plus mandatory insurance — typically 5-30% of the advertised rate.
What is the difference between APR and APY?▾
APR is annualized as 12 × monthly rate (simple — Reg Z convention). APY is the EFFECTIVE rate after compounding: APY = (1 + APR/n)^n − 1. For monthly compounding, 12% APR = 12.6825% APY. Banks disclose APR on loans (Reg Z) and APY on savings accounts (Reg DD) — you need to know which one applies.
How does Newton-Raphson IRR solve for APR?▾
IRR (Internal Rate of Return) is the discount rate that makes the present value of cash flows equal to zero. There is no closed-form solution — Newton-Raphson iterates: start with a guess, compute the value of the equation at that rate, adjust by derivative, repeat until convergence (~5-10 iterations). The calculator uses tolerance 1e-10.
When can the BR CET be considered abusive?▾
Brazilian jurisprudence (não regulação direta) has accepted contractual revision when CET exceeds 1.5× the market median for the loan type. The calculator flags this as "above abusive threshold" — see the Resolução 4.881/2020 + CDC (Lei 8.078/1990) for legal framework. This is not a hard rule; consult a consumer-rights lawyer for material amounts.
What does the US Right of Rescission protect?▾
TILA § 1635 (15 USC) gives you 3 business days after consummation of a principal-dwelling loan to rescind without penalty. If lender disclosures are incomplete or inaccurate, the window extends to 3 years. This is why lenders are very conservative about TRID/Loan Estimate timing — a defective disclosure can void the loan.
How does CET differ from APR mathematically?▾
Same Newton-Raphson IRR engine. Different annualization: CET uses compound (1 + i_monthly)^12 − 1; APR uses simple 12 × i_monthly. For 1.5%/month, CET = 19.56% AA; APR = 18% AA — the ~1.5pp gap is the compounding effect. Both are correct under their respective regulatory regimes.
Are optional insurance products required to enter CET/APR?▾
NO. Both regimes explicitly exclude OPTIONAL insurance. Only insurance that is a CONDITION of the credit (PMI in US for <20% down; DFI/MIP in BR for property loans; prestamista when bank requires it) enters APR/CET. If the bank tries to bundle "credit-protection insurance" as optional, you can refuse — and that refusal does not affect the rate.
How do I detect a deceptive advertisement?▾
Run the calculator with the advertised rate, your principal, term, and fees. If the gap exceeds 25-50% (severity moderate-severe), the advertisement is materially misleading. BR Resolução 4.881 Art. 8º requires that ads mentioning interest rate ALSO mention CET — if it does not, that is a regulatory violation. CFPB has done enforcement against US lenders for under-disclosure > 0.125pp on mortgages.
Why does this calculator show 23 BR states / 5 BR loan types but only ~5 US loan types?▾
BR loan types reflect the structural differences (consignado, rotativo, etc.) — different rates, different fee structures, different markets. US is more flat: personal/auto/mortgage/credit-card cover ~95% of consumer credit. The market benchmarks come from BCB SCR (BR) and Federal Reserve G.19 + Bankrate (US), updated quarterly.
Sources & references
Cross-check every number in this calculator against the primary sources below.
- OfficialCMN Resolução 4.881/2020 — texto integral (BCB)In force: 2020-12-23
- OfficialTILA — 15 USC §§ 1601 et seq.
- OfficialRegulation Z — 12 CFR Part 1026 (full text)In force: 2026-04-08
- OfficialCFPB — TILA Examination Manual
- OfficialReg Z Appendix J — APR formula
- OfficialLei 10.962/2004 — divulgação CET
- OfficialLei 4.595/1964 — Sistema Financeiro Nacional
- OfficialDecreto 6.306/2007 — IOF
- OfficialLei 8.078/1990 — Código de Defesa do Consumidor
- OfficialBCB — Calculadora do Cidadão
- OfficialDodd-Frank Wall Street Reform Act 2010
- OfficialTruth in Savings Act (Reg DD) — APY disclosure rules
- OfficialFederal Reserve G.19 — Consumer Credit
- OfficialBCB SCR — Sistema de Informações de Crédito
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