APR Calculator

Loan amount:

Enter the amount used in the repayment quote, before any upfront finance charge.

Upfront finance charges:

Use 0 when the payment quote has no upfront charges to include.

Fee treatment:

Choose how the entered charge affects the borrower cash flow used for APR.

Scheduled payment:

Use the recurring payment from the quote, such as 322.00.

Payment schedule:

Enter the number of payments and the regular frequency.

{{ warning }}

Final payment:

Keep equal payments for ordinary installment quotes, or enter the exact final payment.

Custom final payment:

Enter the final installment exactly as disclosed in the payment schedule.

Quoted note rate:

Optional; enter the advertised interest rate to see the fee-driven APR spread.

% / yr

Scenario label:

Use a short label such as Credit union quote or Dealer offer A.

Metric	Value	Disclosure use	Copy
{{ row.label }}	{{ row.value }}	{{ row.note }}

Priority	Review item	Evidence	Copy
{{ row.priority }}	{{ row.item }}	{{ row.evidence }}

Payment	Installment	APR interest	Principal	Balance	Period	Copy
{{ row.paymentNumber }}	{{ row.paymentDisplay }}	{{ row.interestDisplay }}	{{ row.principalDisplay }}	{{ row.balanceDisplay }}	{{ row.periodLabel }}

No payment-pressure chart is available for the current inputs.

No balance-runoff chart is available for the current inputs.

Export to PDF Fullscreen

Embed:

Customize

Include current inputs

Size

Advanced

Width

Height

Aspect ratio

Max height

Collapsible embed

Allow fullscreen

Referrer policy

Sandbox tokens

Annual percentage rate, usually shortened to APR, turns a loan's payment stream and finance charges into a yearly borrowing-cost measure. It matters because two quotes can show the same loan amount and similar payments while giving the borrower different usable cash at funding.

A note rate focuses on interest charged on the principal. APR widens the comparison to include timing and eligible upfront charges, so a loan with origination fees or points can show a higher annual cost than the advertised rate suggests.

Loan cash flow timeline showing cash received, regular payments, and a final payment.

APR is useful for installment quotes, vehicle loans, personal loans, and any simple payment schedule where the borrower wants to compare cash received with scheduled payments. It is less useful when the real contract has changing rates, skipped-payment features, optional products, taxes, late fees, or charge treatment that the simple cash-flow model does not include.

Finance results here are educational planning outputs, not legal disclosures or financial advice. Use them to understand a quote and ask sharper questions, then rely on the lender's official documents for binding terms.

Technical Details:

APR for a fixed payment stream comes from the periodic rate that discounts all scheduled payments back to the net proceeds received at funding. When prepaid finance charges are deducted, net proceeds are lower than the face loan amount; when charges are financed, the full loan amount remains the proceeds basis because the entered payment stream is treated as already reflecting those charges.

The nominal APR shown by this calculator annualizes the solved periodic rate without compounding. The effective annual rate compounds that same periodic rate across the selected number of periods per year, so it will usually be slightly higher when the periodic rate is positive.

Formula Core

The present-value equation solves for the periodic rate r, then multiplies that rate by the number of payment periods in a year.

N = \sum_{t = 1}^{n} \frac{P_{t}}{{(1 + r)}^{t}}

APR = r \times m

APR calculation symbols and frequency mapping
Symbol or term	Meaning	How it is used
N	Net proceeds basis	Loan amount minus upfront finance charges when fee treatment is prepaid; otherwise the loan amount.
P_t	Payment in period t	Regular scheduled payment, with the final payment replaced when a custom final installment is entered.
r	Solved periodic rate	Nonnegative rate found by present-value solving.
m	Periods per year	Monthly 12, semi-monthly 24, biweekly 26, weekly 52, or quarterly 4.

A $10,000 loan with $300 deducted upfront, 36 monthly payments of $322, and prepaid fee treatment uses $9,700 as net proceeds. The payment stream totals $11,592, the modeled finance charge is $1,892, the solved periodic rate is about 0.9968% per month, and the modeled nominal APR is 11.96%.

APR validation and warning conditions
Condition	Result behavior	User check
Prepaid fees are greater than or equal to loan amount	Net proceeds are not positive	Confirm that the charge was not already financed or entered twice.
Total payments are below net proceeds	A nonnegative APR cannot be solved	Check payment amount, count, final payment, and fee treatment.
Payment count reaches 600	The count is capped for browser performance	Use a shorter or aggregated schedule for rough comparison.
Quoted note rate is entered	Cost Review Notes shows the spread in percentage points	Use the spread to inspect how much fees and timing lift the APR estimate.

Everyday Use & Decision Guide:

Start from the quote exactly as it is written. Enter the loan amount, upfront finance charges, fee treatment, scheduled payment, payment count, and payment frequency before looking at the APR Disclosure Ledger.

Use prepaid or deducted fee treatment when the borrower receives less cash at funding or pays a charge at closing. Use financed in payment when the charge is already inside the installment amount and the borrower receives the full face amount.

Choose a custom final payment only when the quote names a different last installment.
Add the quoted note rate when you want Cost Review Notes to show the APR spread.
Use the Payment Schedule to confirm the payment count and final balance path.
Use the Payment Pressure Map to see how small installment changes move the modeled APR.
Use the Balance Runoff Curve when the timing of interest and principal paydown matters to the review.

A high spread over the note rate should slow the review, not prove an error. Recheck fee treatment, payment frequency, and the final payment before comparing two offers.

Step-by-Step Guide:

Enter Loan amount as the face amount or cash advanced before prepaid finance charges are deducted.
Enter Upfront finance charges, then set Fee treatment to prepaid or financed so the Net proceeds basis matches the quote.
Enter Scheduled payment, Payment count, and Payment frequency. The summary should change from an input-review message to a modeled APR when the payment stream can be solved.
Open Advanced only when needed. Use Final payment for a different last installment and Quoted note rate for spread comparison.
Read Modeled nominal APR, Effective annual rate, Net proceeds basis, and Total of payments in the APR Disclosure Ledger.
If a warning appears, fix the named issue before comparing offers. Common recovery checks are prepaid fees below the loan amount, payment amount above zero, and total payments high enough to repay the net proceeds.

Interpreting Results:

Modeled nominal APR is the main comparison number for the entered cash flows. Effective annual rate shows the compounded yearly equivalent, and Modeled finance charge shows total payments minus net proceeds.

Do not read the APR estimate as a legal disclosure. Actual disclosure rules can depend on product type, timing, excluded charges, rounding tolerances, and other contract terms.

Verify the result by checking Net proceeds basis against cash received, Total of payments against the schedule, and any APR runs above the quoted note rate note against the lender's fee details.

Worked Examples:

Typical installment quote. A $10,000 loan with a $300 prepaid charge and 36 monthly payments of $322 gives a Net proceeds basis of $9,700. The APR Disclosure Ledger shows Modeled nominal APR at 11.96%, Effective annual rate at 12.64%, and Modeled finance charge at $1,892.

Short term with a large fee. A $5,000 loan with $600 deducted upfront and six monthly payments of $900 gives only $4,400 in net proceeds. The same math produces a 74.22% Modeled nominal APR, which is why Cost Review Notes flags short terms and material upfront charges.

Input problem. If a $10,000 loan is paired with 12 monthly payments of $700, total payments are below the net proceeds. The result cannot solve a nonnegative APR, so the recovery path is to check whether payment count, payment amount, or a final balloon payment was omitted.

FAQ:

Why can APR be higher than the note rate?

APR can rise above the note rate when upfront finance charges reduce net proceeds or when payment timing makes the entered stream imply a higher yearly cost.

What is the difference between modeled nominal APR and effective annual rate?

Modeled nominal APR multiplies the solved periodic rate by periods per year. Effective annual rate compounds that periodic rate over the same frequency.

Why does the tool say APR cannot be solved?

The usual causes are net proceeds at or below zero, no positive payment stream, or total payments below net proceeds. Check loan amount, fee treatment, scheduled payment, payment count, and final payment.

Can this replace the lender's APR disclosure?

No. Use the result to audit assumptions and compare quotes, then rely on official loan documents for binding disclosure and legal treatment.

Glossary:

APR: Annual percentage rate, a yearly borrowing-cost measure based on the entered cash flows.
Net proceeds basis: The cash-flow basis discounted against payments, reduced by prepaid finance charges when selected.
Periodic rate: The rate solved for one payment period before annualization.
Finance charge: Total payments minus net proceeds in this model.
Effective annual rate: The compounded yearly equivalent of the solved periodic rate.

References:

What is the difference between a loan interest rate and the APR?, Consumer Financial Protection Bureau, January 30, 2024.
Regulation Z section 1026.22, Determination of annual percentage rate, Consumer Financial Protection Bureau.