APR Is a Rate Convention and a Disclosure Term
The conversion tabs treat APR as a nominal annual interest rate. A disclosed borrowing APR relates the amount and timing of money received to the payments owed, and can include qualifying charges. These are different tasks: converting a fee-inclusive APR to a compounded yield does not reveal a savings return or reproduce a lender’s disclosure.
Nominal Rate and Effective Yield
For a positive nominal rate, compounding more than once per year increases the effective annual yield. At zero the two are equal. Constructed example: 12% nominal compounded monthly gives (1.01)^12 − 1 = approximately 12.6825%. This assumes a constant rate, reinvested interest and no fees; it is not a quoted account offer.
Match the Inputs to the Cash Flows
- For conversions, enter the nominal rate or effective yield and select one of eight compounding frequencies. Conversion results support nominal rates from 0% to 1,000%.
- For Loan APR, enter the gross advance, whole monthly term, fixed payment and prepaid finance charges. The payment starts one month after funding. Charges are subtracted from proceeds to solve the rate and included in Total Amount Paid. Fees must be nonnegative and less than the advance.
- For Card Payoff, enter a positive balance, nonnegative APR and fixed monthly payment. The simplified model adds one month of interest and then subtracts payment. It stops only when repaid; otherwise no payoff result is shown after the 600-month limit.
Results update as you type. All calculations are local; no lender account is accessed. Amounts are formatted in USD without conversion.
Formulas and Solver Bounds
Using decimal rates, effective yield = (1 + j/m)^m − 1 and nominal j = m × ((1 + yield)^(1/m) − 1). Continuous compounding uses exp(j) − 1 and ln(1 + yield). Enter percentages in the fields: 12 means 12%, not 0.12%.
For an equal-payment loan, net proceeds = payment × (1 − (1 + r)^(-n)) / r. The zero-rate limit is payment × n. The tool brackets r from 0 to 1 per month, uses bisection, and reports 12r as annual APR. It rejects unavailable solutions and terms outside 1–1,200 whole months. It does not silently return a capped rate.
Why a Card Statement Can Differ
The card model uses a monthly rate of APR/12 with no spending, fees, promotional expiry or rate changes. Many issuers calculate interest daily from daily balances and apply different rates to purchases and cash advances. A grace period may affect purchase interest. Payment timing and allocation can therefore change actual interest from this simple illustration.
Compare Like-for-Like Scenarios
Keep advance, term, payment dates and fee treatment consistent when comparing loans. Do not enter financed fees again as prepaid charges. Not every closing cost is included in legal finance charges; this tool does not determine that classification, handle odd first periods or provide regulatory APR disclosure. Check the lender’s Loan Estimate or contract.
Primary sources: CFPB Regulation Z §1026.22, interest rate versus APR, and credit-card interest calculations.