Compare borrowing cash flows under an explicit timing convention. Equal periods produce nominal and effective annual estimates; exact dates produce an Actual/365 annual economic yield. Neither certifies a lender disclosure.

Why fees can change APR

An interest rate describes interest charged on a balance, while APR can also reflect charges connected to obtaining credit. If a lender deducts a fee before disbursement, the borrower receives less cash while owing the scheduled payments, so the solved borrowing rate rises.

Fee treatment is product- and jurisdiction-specific. Classify a fee according to the comparison you want to make and verify the lender's official disclosure before deciding.

How the numeric solver works

Received cash is positive and paid cash negative. Only the equation nets simultaneous flows; the ledger and totals retain gross advances, repayments and fees.

Bracketed bisection works in log-rate space and accepts a result only after a scale-relative discounted-cash residual check. Small rate intervals alone do not prove convergence. Unsupported or ambiguous schedules produce a diagnostic with inputs retained.

Nominal APR versus effective annual rate

For equal periods, nominal APR multiplies the periodic rate by periods per year; effective annual rate compounds it. For dated flows, actual UTC days divided by 365 define time and the annual economic yield is shown separately.

Actual/365 is not a substitute for the unit-period and odd-period rules of Regulation Z Appendix J, or another jurisdiction’s fee, timing and rounding requirements.

When this model is not enough

The calculator solves entered cash flows, not a loan contract. Dated mode supports calendar timing under Actual/365 but does not certify odd-period legal APR. Variable-rate forecasts, revolving credit, tax effects and product-specific regulatory fee classification are not modeled.

Review the actual lender disclosure and the rules applying to the product. A negative result can be mathematically valid; it does not establish eligibility for a subsidy or rebate.