Payment (monthly)
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Loan Truth-in-Lending Toolkit
APR Calculator — Find the True Cost of Any Loan
The interest rate on the sticker is never the whole story. Enter the nominal rate plus fees and this calculator solves the true Annual Percentage Rate — the uniform, legally-defined cost-of-credit measure (TILA / Regulation Z) — so you can compare car loans, mortgages and personal loans honestly.
Educational estimate — not professional financial advice. Results illustrate how APR works; your lender's official Truth-in-Lending disclosure governs your loan. Consider consulting a licensed financial professional before borrowing.
True APR from loan terms
Actuarial method (Regulation Z Appendix J): the periodic rate i that equates the amount financed to the present value of all payments, annualized as i × payments/year.
Full amount borrowed, before fees are subtracted.
Origination, processing, points… anything you pay (or that is deducted) to get the loan. These shrink the amount financed and push APR above the nominal rate.
True APR
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Amount financed
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Total of payments
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Finance charge (interest + fees)
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Interest alone
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Effective annual rate
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Cost per $1,000 borrowed
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Fee drag (APR − nominal)
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⚠️ Educational estimate — not professional financial advice. Under the Truth in Lending Act your lender must disclose the official APR; it is considered accurate if within ⅛ of a percentage point of the actuarial value.
Compare loan offers side by side
Lenders advertise nominal rates — APR levels the field because it folds fees in. Add up to 4 offers; the tool ranks by lowest APR and by lowest total cost (they don't always agree).
⚠️ Educational estimates — not professional financial advice. APR comparison assumes identical payment timing and no prepayment penalties; always read the lender's Truth-in-Lending disclosure.
Short-term / fee-based APR
For payday loans, cash advances and merchant cash advances — credit priced as a flat fee for a few days or weeks, where the nominal-rate machinery doesn't apply.
APR = ( fees + interest ) ÷ principal ÷ days × 365 × 100
Simple APR
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Daily cost rate
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Cost per $100 borrowed
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Total repayment
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Equivalent monthly rate
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⚠️ Educational estimate — not professional financial advice. Short-term credit is among the most expensive borrowing available; this illustration uses the CFPB-style simple-APR convention.
APR → APY
Convert a nominal APR to the effective annual yield with compounding.
APY = ( 1 + APR ÷ m )m − 1
Effective APY
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APY → APR
Convert an effective yield back to the nominal APR.
APR = m × ( (1 + APY)1/m − 1 )
Nominal APR
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Two-way quick converter. A dedicated APR↔APY conversion suite (with continuous compounding, EAR tables and rate-equivalence charts) is planned as a separate tool.
① What “true APR” actually means
Under the U.S. Truth in Lending Act (TILA) and its implementing rule Regulation Z (12 CFR 1026.22), the annual percentage rate is “a measure of the cost of credit, expressed as a yearly rate, that relates the amount and timing of value received by the consumer to the amount and timing of payments made.” It is deliberately not the same thing as the interest rate: the APR folds in prepaid finance charges (origination fees, points, certain closing costs) by computing against the smaller amount financed — what you actually receive — rather than the headline loan amount.
This calculator implements the actuarial method from Regulation Z Appendix J: it finds the periodic rate i that makes the present value of your payment stream exactly equal the amount financed, then annualizes it as i × payments per year. With zero fees, the math collapses exactly to the nominal rate — a good sanity check you can try yourself. With fees, APR always lands above the nominal rate, and the gap (“fee drag”) is the honest price of those fees expressed as a rate.
amount financed = Σ paymentk ÷ (1 + i)k → APR = i × payments/year × 100
② Worked examples (verified against the formula)
Car loan — fees push APR up
$20,000 · 8% nominal · 60 months · $500 origination fee
Payment $405.53/mo · True APR 9.0781%
The $500 fee is deducted from what you effectively receive ($19,500 financed), so the same $405.53 payments imply a 9.08% yearly cost — 108 basis points of fee drag.
Mortgage — points vs. rate
$350,000 · 6.75% nominal · 30 years · $8,000 in points & fees
True APR 6.9772% · Finance charge $475,234
Points buy the nominal rate down but lift the APR: run both offers through the Compare tab to see which is cheaper over your actual holding period.
Payday loan — flat-fee pricing
$100 borrowed · $15 fee · 14 days (classic CFPB illustration)
Simple APR 391.07%
Simple APR = (15 ÷ 100 ÷ 14) × 365 × 100. Flat fees over days — not years — are why short-term credit shows triple-digit APRs.
③ Methodology & limits
How payments are computed: standard amortization on the full principal at the nominal periodic rate: PMT = P·i / (1 − (1+i)−n). The APR solver then re-prices those payments against the amount financed (principal minus prepaid fees) using Newton iteration with a bisection fallback — the actuarial method of Reg Z Appendix J.
What's included in “fees” here: anything the lender charges you to obtain the credit (origination, processing, discount points, certain mortgage insurance premiums). Real-estate transactions have a long list of charges that Regulation Z explicitly includes or excludes — this tool treats whatever you type as a prepaid finance charge.
Assumptions: equal periodic payments starting one full period after consummation, fixed rate for the whole term, no prepayment, no late fees, no variable-rate adjustments. Adjustable-rate, interest-only, balloon and graduated-payment loans need their own disclosures — the disclosed APR on those is a composite/blended figure.
Accuracy: TILA deems a disclosed APR accurate if it is within ⅛ of a percentage point (¼ point for irregular transactions) of the actuarial value.
APR formula — both faces: the simple (flat-fee) form is APR = (fees + interest) ÷ principal ÷ days × 365 × 100; the installment form is the actuarial equation above. In Excel the same actuarial result is =RATE(nper, pmt, -amount_financed)×12 with amount_financed = principal − fees. Supported payment frequencies: monthly, semi-monthly, bi-weekly (biweekly), weekly, quarterly and annual. Every result also shows the cost per $1,000 borrowed — the finance charge per 1000 of principal — for quick comparison.
④ Related tools — scope boundaries
APR vs APY: this tool prices borrowing (APR = cost of credit). The effective yield you earn on savings is the APY concept — a dedicated APY tool is planned separately. Intent is different: borrower cost vs saver yield.
Need the payment schedule itself? See loan amortization for month-by-month principal/interest splits, or auto loan amortization schedule for car-specific schedules.
Shopping for a specific loan type? bank loan calculator and personal loan calculator estimate payments; mortgage calculator with extra payments and mortgage payment with taxes & insurance cover home loans with escrow.
Looking for a basic / simple APR calculator? It's built in: the Short-term APR tab is the easy one-line version (amount, fee, days → APR), and the True APR tab's presets keep the full version to five fields. “Basic” means fewer inputs, not different math — which is why it lives here instead of on a separate page. Credit-card APR note: cards disclose APR as a daily periodic rate (APR ÷ 365) on revolving balances; this tool's True APR tab prices installment loans, not revolving daily-rate math.
Scope of THIS tool: true-cost APR math + offer comparison. It does not generate amortization tables, predict approval odds, or recommend lenders.
⑤ Frequently asked questions
⑥ APR vs interest rate: how to actually compare loan offers
The interest rate prices only the borrowed balance per period; the APR prices the whole deal. Under the Truth in Lending Act (Regulation Z), the APR folds prepaid finance charges — origination fees, discount points, certain closing costs — into one yearly rate by measuring your payments against the smaller amount financed (what you effectively receive) instead of the headline loan amount. With zero fees the two numbers are identical; with fees, APR is always higher, and the gap — the fee drag — is the honest price of those fees expressed as a rate. On a $300,000 30-year loan at 6.5%, adding $6,000 in fees lifts the true APR from 6.5000% to 6.6953%: 19.53 basis points of fee drag on the identical $1,896.20 monthly payment.
To compare offers correctly, hold the inputs constant: same loan amount, same term, same payment timing — then the lower APR is the cheaper loan if you keep it for the full term. That last condition is the one everyone misses. APR spreads upfront fees over the entire term, so a low-rate/high-fee offer can show the lowest APR yet cost more if you sell or refinance early. Take a $400,000 30-year loan: offer A at 6.25% with $18,000 in points (APR 6.6917%) versus offer B at 6.75% with no fees (APR 6.7500%). A wins on APR and saves $131.52/month — but the $18,000 upfront takes 136.9 months, about 11.4 years, to earn back. Move or refinance before then and B was cheaper despite its higher APR. Rule of thumb: compare by APR for loans you'll hold to maturity; compare by break-even timing for anything shorter.
Two more honest limits. First, Regulation Z excludes certain real costs from the finance charge — appraisal, title, recording fees and taxes in mortgage transactions are generally excluded when bona fide and reasonable, and seller-paid points don't count toward your APR — so the disclosed APR can understate your all-in closing cost. Second, TILA deems a disclosed APR accurate within ⅛ of a percentage point (¼ point for irregular transactions), so a quoted 6.70% could legally be 6.68% or 6.72% under the hood. This calculator shows more decimals than any disclosure ever will — use that precision to compare, not to split hairs.
Reference: $300,000 · 30 years · 6.5% nominal — same payment, different true cost
| Upfront fees | Amount financed | Monthly payment | True APR | Fee drag | Total finance charge |
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| $0 | $300,000 | $1,896.20 | 6.5000% | 0.0000 pp | $382,633 |
| $6,000 | $294,000 | $1,896.20 | 6.6953% | 0.1953 pp | $388,633 |
| $12,000 | $288,000 | $1,896.20 | 6.8971% | 0.3971 pp | $394,633 |
Actuarial method (Reg Z Appendix J), verified against the engine above. The payment never changes — only the amount financed does, which is exactly why APR exists.
⑦ Worked examples (step by step)
Auto loan — fee drag, by hand
$25,000 · 7.5% nominal · 60 months · $600 origination fee
1. Monthly rate: 0.075 ÷ 12 = 0.00625.
2. Payment: 25,000 × 0.00625 ÷ (1 − 1.00625−60) = $500.95/mo.
3. Amount financed: 25,000 − 600 = $24,400.
4. Solve 500.95 × (1 − (1+i)−60) ÷ i = 24,400 → i = 0.0071078 → APR = 8.5294%.
Fee drag: 102.94 basis points. Total paid $30,056.92.
Offer shootout — when the lower APR loses
$400,000 · 30 years. A: 6.25% + $18,000 points. B: 6.75% + $0 fees.
A: payment $2,462.87, APR 6.6917%, finance charge $504,633.
B: payment $2,594.39, APR 6.7500%, finance charge $533,981.
Upfront gap $18,000 ÷ $131.52/mo savings = 136.9 months ≈ 11.4 years to break even.
Sell or refinance before ~11.4 years and B was cheaper — despite the higher APR.
Sanity check — zero fees
Any loan with no upfront fees must produce APR = nominal rate exactly.
Enter $300,000 · 6.5% · 360 months · $0 fees in the True APR tab: the solver returns 6.5000%, drag 0.0000 pp. If a calculator can't reproduce this, don't trust its fee math either.
This is the actuarial identity: with amount financed = principal, the solution rate is the nominal rate.
⑧ Practical tips
Compare APR, not rate — then compare break-even. Normalize every offer to APR for full-term holds; for shorter holds, divide the upfront-fee gap by the monthly payment savings to get your break-even month.
Negotiate the inputs, not the APR. Lenders rarely "lower your APR" directly, but origination fees, points, and add-ons are negotiable — every dollar of fees removed lowers the APR even when the rate doesn't move.
Ask what the APR excludes. Appraisal, title, recording, and tax charges are generally outside the finance charge — get the all-in cash-to-close separately so the APR doesn't hide them.
Short-term credit: read APR as a warning label. A $15 fee on $100 for 14 days is 391.07% APR — the fee looks small in dollars precisely because the term is short.
Don't over-precision shop. TILA tolerates ⅛ point of disclosure error, so treat 6.69% vs 6.71% as a tie and decide on fees, service, and lock terms instead.
Refinancing resets the fee clock. A refi at a lower rate with big closing costs restarts fee drag from zero — run both the old and new loan through the Compare tab before signing.
Free tool by NRTechStudio