# How APR and APY Actually Differ — And Why It Matters
Two financial products can carry the same stated interest rate and cost you very different amounts of money. The difference is compounding frequency — and whether a company is quoting you APR or APY.
This is not an accident. Financial institutions use the version that makes their product look better. Lenders quote APR. Savings accounts quote APY. Understanding the translation between them is one of the most practically useful things you can know.
APR: Annual Percentage Rate
APR is the interest rate expressed annually, without accounting for compounding within the year. On a credit card with 24% APR, the monthly rate is 24% ÷ 12 = 2%. Interest is calculated on your daily balance, but when you see "24% APR," the compounding effect within the year is not built into that number.
The law requires lenders to disclose APR, which is why it appears on credit cards, mortgages, and auto loans. It is a useful standardized number for comparison — but it understates the true annual cost when interest compounds within the year.
APY: Annual Percentage Yield
APY includes compounding. It tells you what you will actually earn (or owe) over a full year, assuming you do not make withdrawals or extra payments. A savings account with 5% APR compounding monthly has an APY of approximately 5.12% — you earn slightly more than 5% because each month's interest earns interest in subsequent months.
On the earning side, banks advertise APY because 5.12% sounds better than 5%. On the borrowing side, lenders advertise APR because 24% sounds better than the ~26.8% APY equivalent.
The formula
The relationship between APR and APY is:
**APY = (1 + APR/n)ⁿ - 1**
Where n is the number of compounding periods per year (12 for monthly, 365 for daily).
For a credit card with 22% APR compounding daily: APY = (1 + 0.22/365)^365 - 1 = **24.6%**
That gap — 22% vs. 24.6% — represents the true annual cost of carrying a balance. The card company quotes 22% because they are required to quote APR. Your actual cost is closer to 24.6%.
Expense Ratio Drag
A 1% fee compounded over 30 years can eat 25-30% of final wealth. The headline expense ratio looks tiny — its lifetime impact rarely is.
That's 16% of your fee-free FV — gone, just to fees.
Educational illustration — not financial advice. Math: @/lib/finance/investing.ts. Real fees compound on the balance every year — this calculator approximates that with a constant-rate net return.
Where this matters most
**Credit cards:** Daily compounding is standard. The APY on most credit cards runs 1.5–3 percentage points above the stated APR. On a large, persistent balance, this gap is meaningful.
**Mortgages:** Monthly compounding is typical. The APY is close to APR (about 0.1–0.2 points higher at prevailing rates). The APR disclosure on mortgages also includes fees, making it a better apples-to-apples comparison than the interest rate alone.
**Savings accounts and CDs:** Daily or monthly compounding is standard. High-yield savings accounts advertise APY — that is the number to compare across institutions. When a bank shows you a rate, check whether they are quoting APR or APY. The difference is usually small for savings but worth confirming.
**Auto loans:** Simple interest is common for auto loans, meaning interest does not compound — the stated APR is the true annual cost. This makes auto loan APR more honest than credit card APR.
How to compare products honestly
When comparing any two interest rates: 1. Convert both to APY using the same compounding frequency assumption. 2. For debt products, the APY is your actual annual cost. 3. For savings products, the APY is your actual annual gain.
The calculator above does this conversion automatically. Enter any APR and compounding frequency to see its true APY equivalent.
The practical takeaway
For most everyday borrowing decisions — should I take this credit card? is this personal loan better than that one? — APR comparisons are fine because you are comparing within the same product category with the same compounding convention.
The comparison breaks down when you cross categories. A credit card at 22% APR and a personal loan at 22% APR are not equivalent if the credit card compounds daily and the personal loan compounds monthly. Convert both to APY first.
For savings decisions, always compare APY to APY. A bank advertising 4.8% APR compounding monthly offers less than a bank advertising 4.8% APY — the first is actually 4.91% APY, slightly better, but the point is that APY is the honest number.
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*Related: [The true cost of minimum payments](./true-cost-of-minimum-payments) shows how daily compounding drives the real cost of carrying a balance. [Balance transfer math](./balance-transfer-math) applies this to 0% promotional rate decisions.*
Frequently Asked Questions
what is the difference between APR and APY
APR is simple interest on an annual basis, while APY includes compound interest and reflects actual costs. For the same rate, APY is always higher and more accurately represents what you'll actually pay, especially for frequently compounding debt like credit cards.
why do banks show APR instead of APY
APR appears lower and more attractive to borrowers, so lenders prefer displaying it on credit cards and loans. However, APY is the more honest figure that reveals true interest costs, which is why regulators require disclosure of both for transparency.
does APY or APR matter for credit cards
APY matters more for credit cards because interest compounds daily. Most cards advertise APR, but your actual cost is based on daily APY calculations, making the real rate higher than advertised and why minimums don't dent principal quickly.