How this instrument works
Annual percentage rate is the number a US card issuer, retailer or payday lender is required to print on a credit agreement, and it is built from the simplest arithmetic available: take the percentage that applies to one billing cycle and multiply by how many cycles happen in a year. A card charging 1.5% each month is disclosed at 18% APR not through any deeper calculation but because Regulation Z, which implements the Truth in Lending Act, defines APR as exactly that — a nominal figure, not a compounded one.
The formula stays this simple on purpose. APR exists so a shopper can hold two credit offers side by side without doing the arithmetic themselves, and a straight multiplication is the version regulators settled on for disclosure — even though it understates what debt actually costs once interest starts compounding on interest already added. That harder, compounded figure has its own name, effective annual rate, and its own instrument; APR never claims to be it.
Reading a periodic rate off a statement and multiplying is also how the number goes wrong for people. A payday loan charging $15 on every $100 borrowed for two weeks looks like a 15% fee, but 26 two-week periods fit in a year, so the nominal APR clears 390% — a figure the formula reports honestly and a borrower glancing only at the $15 tends to miss entirely. The formula is not the problem; the periodic rate people plug into it is usually the part nobody has scrutinized.
- Find the percentage charged each billing cycle on your statement or contract and enter it as Rate per period, %.
- Count how many of those cycles occur in a year — 12 for monthly, 52 for weekly, 26 for biweekly — and set Periods per year.
- Read APR (nominal annual rate) — the disclosure-format figure, built by simple multiplication with no compounding folded in.
- Change Periods per year alone, holding the periodic rate fixed, to see how billing frequency by itself moves the annualized number.
Worked example — an 18% card from a 1.5% monthly rate
A credit card agreement lists a monthly periodic rate of 1.5%, charged twelve times a year. Enter 1.5 into Rate per period, % and 12 into Periods per year, and the instrument multiplies them straight through: 1.5 times 12 equals 18, so APR (nominal annual rate) reads 18%. That is the figure printed on the cardmember agreement, and Regulation Z requires the issuer to disclose it alongside the periodic figure itself.
That 18% is nominal, not compounded — the same 1.5% charged monthly actually grows a carried balance by close to 19.56% over a year once interest capitalizes each cycle, the effective annual figure an APY-style calculation would report instead. The gap, roughly a point and a half here, is exactly what compounding costs a borrower that a simple annualized number never shows on its own.
Questions
Why isn't APR the same as compound interest?
Because APR is built by simple multiplication — periodic rate times periods per year — while compounding lets each period's interest earn interest on itself. An 18% APR credit card charging 1.5% monthly actually grows a carried balance by close to 19.56% over a year once compounding is included; APR is the disclosure number, not the compounded one. Reach for an effective-rate or APY instrument when the compounded figure is what you actually need.
What periods per year should I use for a weekly or biweekly loan?
Use 52 for a loan charged every week and 26 for one charged every two weeks — that is how many periods genuinely fall in a year, not an estimate. Payday loans are the case where this matters most: a $15 charge on $100 for two weeks is a 15% periodic rate, and multiplying by 26 biweekly periods produces a nominal APR above 390%, far higher than the flat fee alone suggests.
Does this APR figure already include fees?
Only whatever fees are already folded into the periodic rate you enter — this instrument does not add anything on top of it. Regulation Z requires lenders to roll certain finance charges into that periodic figure before disclosing APR, but a card's separate annual fee, a loan's origination charge, or a payday lender's rollover fee sit outside this arithmetic unless you have already worked them in yourself.
Why do two loans with the same APR feel different to pay off?
APR only annualizes a percentage; it says nothing about a loan's term, balance, or whether interest compounds during repayment. A two-week payday loan and a year-long installment loan can share a nominal APR while carrying entirely different total costs, because APR compares the percentage alone, not the schedule of payments built on top of it. Compare full repayment schedules, not just the annualized figure, before treating two APRs as equivalent offers.
Can Periods per year be something other than 12, 52, or 26?
Yes — enter whatever matches how the contract actually charges interest, including 4 for quarterly, 365 for daily, or 1 for a rate already stated annually. The field accepts any positive count, because APR disclosure rules cover contracts with unusual billing cycles, not only the common monthly card cycle.
Is a lower APR always the cheaper way to borrow?
Not necessarily — APR ignores fees not folded into the periodic rate, the compounding that happens once a balance is carried, and how long the debt stays outstanding. Two offers with identical APRs can produce different total interest depending on term length and repayment pace, so treat APR as a way to compare rates on equivalent terms, not as the single number that settles which loan costs less overall.
References
Read this first: This instrument shows arithmetic, not advice. Real offers add fees, taxes and terms that vary by lender and place — verify the figures against your actual paperwork before deciding anything.