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APR vs APY And Why It Matters

compounding frequency; the same rate quoted two ways

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APR and APY differ because one ignores compounding and the other includes it; the gap widens as compounding happens more often within the year, which is exactly why the label matters.

The mechanism behind the two numbers

APR, or Annual Percentage Rate, is a nominal rate: the stated interest charged over a year, with no assumption about how often interest is added back to the balance. APY, or Annual Percentage Yield, is the effective annual rate, the percentage the balance actually grows after compounding is applied. The relationship between them is captured by one formula:

APY = (1 + APR / n)n − 1

where n is the number of compounding periods per year. When n equals 1, the two numbers are identical. As n climbs, the APY rises above the APR, and the difference grows with the size of the rate itself.

A worked comparison

Take an account advertising 12% and ask what one dollar becomes after one year under different compounding schedules:

On the borrowing side, a credit card at 20% APR compounded daily produces an effective annual rate of roughly 22.1%, several points above the number printed on the monthly statement.

The common misunderstanding

Many borrowers assume that the APR in a loan disclosure already reflects the true yearly cost of borrowing. It does not. APR folds in certain upfront charges such as origination fees and discount points, but it still treats interest as if it accrues only at year-end. On a long-term installment loan with monthly compounding, the effective cost paid each year can sit noticeably above the disclosed APR. APR is honest about fees, but quiet about in-year compounding.

Where the framing breaks down

The APR-versus-APY distinction assumes interest can compound inside the year. Loans calculated on simple interest, where interest is computed on the original principal and never added back to the balance, do not produce a gap at all. Zero-interest promotional financing may also carry an APR that exists only as a regulatory placeholder rather than a real cost. And outside the United States, the term APR sometimes already means what Americans call APY, so cross-border comparisons require reading the fine print rather than the headline number.

The practical rule is what the video closed on: convert both sides of any comparison to the same effective annual figure before deciding. The label is marketing. The compounding is the price.

Transcript

Cram: If two accounts both say twelve percent, they pay the same thing, right? A rate is a rate. Rep: Not quite. Twelve percent APR and twelve percent APY are two different numbers wearing the same costume. Cram: How can the same twelve be two different numbers? Rep: APR is the plain annual rate before compounding. APY is what you actually end up with once compounding is applied. Cram: So the compounding is the whole gap. Rep: Yes. Twelve percent APR compounded monthly works out to about twelve point six eight percent APY. Same label, more money. Cram: Then why would anyone quote the smaller number? Rep: Because it depends who the number flatters. Savings accounts advertise APY because it looks bigger. Loans get quoted as APR. Cram: That feels like a trick. Rep: It is regulated, not random. In the United States lenders must disclose APR, and it folds in certain fees, not just interest. Cram: So on a loan the APR is already the honest number. Rep: Honest about fees, quiet about compounding. Carry a credit card balance and daily compounding pushes the real cost above the stated APR. Cram: So I should compare like for like. Rep: Exactly. Convert both sides to the effective annual figure, then compare. The rate is the label. The compounding is the price.

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