⚡ Financial LiteracyUpdated: September 2, 2026
Annual Percentage Rate (APR) Math: Nominal vs. Effective APR on 14-Day Advances
Reviewed by Consumer Financial Protection & Small-Dollar Lending Editorial Board
The quantitative mathematics of Truth in Lending Act (TILA) calculations: annualized finance charges, 14-day terms, and understanding 391% APR disclosures.
Federal law requires all lenders to disclose loan costs as an Annual Percentage Rate (APR) to allow standardized comparisons, even for two-week emergency loans.
1. The TILA APR Formula
The Standard APR Formula
$$\text{APR} = \left( \frac{\text{Finance Charge (\$)}}{\text{Loan Amount (\$)}} \right) \times \left( \frac{365}{\text{Term (Days)}} \right) \times 100$$ On a $100 loan with a $15 fee for 14 days: $$\text{APR} = \left( \frac{15}{100} \right) \times \left( \frac{365}{14} \right) \times 100 = 0.15 \times 26.0714 \times 100 = 391.07\%$$
| Loan Amount | Finance Fee ($15 per $100) | Loan Term | Disclosed Nominal APR |
|---|
| $100.00 | $15.00 | 14 Days | 391.07% APR |
| $300.00 | $45.00 | 14 Days | 391.07% APR |
| $500.00 | $75.00 | 30 Days | 182.50% APR |
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Consumer Financial Protection & Small-Dollar Lending Editorial Board
Our financial literacy specialists review short-term lending regulations, Truth in Lending Act disclosures, and credit union alternative products to protect consumer rights.
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