The annual percentage rate (APR) is the headline number lenders advertise. The annual percentage yield (APY) is what you actually pay once compounding is factored in. On a 20% APR credit card, the real cost is 21.94% APY. On a 30-year mortgage, a single percentage point difference can add nearly $90,000 in total payments.
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In the spring of 2022, the Federal Reserve began one of the fastest rate-hiking cycles in decades, lifting its benchmark from near zero to above 5% in fourteen months.1 Millions of Americans with variable-rate credit cards watched their APR climb in near-lockstep with each announcement. But the number printed on their statement, the APR, understated what they were actually paying. The real cost ran higher, because credit card interest does not sit still for a year.
Let's start with how the two figures actually differ, because the confusion here is not accidental.
APR is the headline; APY is the reality
The Annual Percentage Rate (APR) is simple annual interest: it tells you how much you would owe over a full year if interest were calculated once and never touched again. Lenders advertise APR because it is always the lower, friendlier number.2
The Annual Percentage Yield (APY) is the effective annual rate once compounding is accounted for. Compounding means interest is calculated on a schedule, and once it accrues, it becomes part of the balance that interest is calculated on next time. When that cycle runs monthly, quarterly, or daily, the result creeps above the headline APR.
The Consumer Financial Protection Bureau requires lenders to disclose APR prominently, which helps comparison shopping, but APY is the figure that tells you what you will actually owe.2
How compounding changes the math
Start with simple interest. Borrow $10,000 at 10% APR with no compounding: after one year you owe $11,000, after two years $12,000. Straightforward.
Now apply the same 10% APR with monthly compounding, which is how most consumer loans actually work. In month one, interest accrues on $10,000 at a monthly rate of 10% divided by 12, which is 0.833%. That is $83.33. The month-two balance is $10,083.33, and interest now applies to that full figure, not the original $10,000. By year one the balance has grown to $10,471, not $11,000 because the rate is 10%, but the effective rate is 10.47%. That gap is the difference between APR and APY.
The formula to convert is straightforward: APY equals (1 plus APR divided by n) raised to the power of n, minus 1, where n is the number of compounding periods per year (12 for monthly, 365 for daily). You do not need to memorize this. You need to know it exists so you ask the lender for it.
What this means on a credit card balance
Take a credit card advertising 20% APR with monthly compounding. The effective APY works out to 21.94%.3 On a $5,000 balance you carry for a full year without making payments:
- Simple interest at the stated APR: $1,000 owed
- Compound interest at the effective APY: $1,097 owed
- Difference: $97
That spread does not sound catastrophic on its own. But credit card debt is rarely held at a static balance for exactly one year. If you carry $5,000 and make only the minimum payment of $100 per month, you will spend roughly 56 months paying it off and hand over about $2,160 in interest along the way, which is 43 cents for every dollar you originally borrowed.3 That is the compounding treadmill in real time.
The savings account lens
Now shift to where compounding works in your favor. A high-yield savings account advertising 4.5% APY is already telling you the compounded rate. Deposit $10,000, and after one year you have earned exactly $450, not slightly less. The APY is the honest number because savings institutions are required to advertise it for deposit products, precisely so you can compare without running the conversion yourself.4
If instead the account advertised 4.5% APR compounded monthly, the effective APY would be 4.60%. The difference on $10,000 over a single year is about $10, which is negligible, but held over 30 years those small differences compound into something significant. A $20,000 deposit earning 4% APY for 30 years grows to roughly $65,000. The same deposit at 2% APY grows to only $36,000. That is almost $30,000 in lost earnings from a 2-percentage-point difference in rate, the same way a 2-point difference on a mortgage costs you $184,000 in extra interest.5
Mortgage rates: where one percentage point is worth six figures
Let's run the numbers on a $400,000 home loan at a 30-year fixed term, since this is where the compounding argument becomes difficult to ignore.
| Rate (APR) | Monthly payment | Total paid | Total interest |
|---|---|---|---|
| 5% | $2,147 | $773,435 | $373,435 |
| 6% | $2,398 | $863,352 | $463,352 |
| 7% | $2,661 | $957,636 | $557,636 |
Moving from 5% to 6% costs $89,917 in total payments over the life of the loan. Moving from 5% to 7% costs $184,201. These are not abstract numbers; they are a new car, or a year of college, or ten years of retirement contributions, gone to a lender because of a rate difference that looked small in the newspaper.5
Mortgages are typically quoted as APR with monthly payments, so the APR-to-APY conversion is already baked in by the time you reach the closing table. The lesson is not the formula; it is the magnitude. Fractions of a percent, held over decades, are large sums.
Compounding frequency matters too
The same 10% APR produces different effective costs depending on how often the lender compounds the interest. Here is what that looks like at a glance:
| Compounding schedule | Effective annual rate |
|---|---|
| Annually | 10.00% |
| Quarterly | 10.38% |
| Monthly | 10.47% |
| Daily | 10.52% |
The spread from annual to daily is only 0.52 percentage points, but on a $10,000 balance held for five years, that difference is about $200. Credit card issuers use daily compounding because it maximizes what you owe; savings accounts often use daily compounding too, because it maximizes what you earn.3 The frequency cuts both ways, and knowing which direction it is cutting is basic financial hygiene.
How to compare two loans the right way
Here is the practical test. Suppose you are looking at two personal loans.
- Loan A: 10% APR, compounded monthly. Effective APY: 10.47%.
- Loan B: 10.5% APR, compounded annually. Effective APY: 10.5%.
Loan A looks cheaper. The APR is lower by half a point. But the effective cost is nearly identical, because Loan B compounds only once per year while Loan A compounds twelve times. APR comparison alone told you the wrong story.
The fix is simple: ask every lender for the APY, or run the conversion yourself using the formula above. You can also use a compound interest calculator to run the full-term cost side by side at /tools/compound-interest before you commit to anything.
For savings products, federal law already requires APY disclosure on deposit accounts, which is why your savings account statement shows APY prominently.4 For loans, it often takes asking, but every legitimate lender can provide it.
The part most outlets skip
Overall, the distinction between APR and APY is not a technical footnote. It is the difference between what a lender says you will pay and what you actually pay, and the gap compounds over time by design. The rate you lock in on a mortgage or a car loan today gets applied to a growing or shrinking balance for years, and a few tenths of a point at the start will translate into hundreds or thousands of dollars at the finish.5
The next time you see an advertised rate, before you sign anything, ask: is this an APR or an APY, and how often does interest compound? That single question, put to every lender you are comparing, will tell you more about the true cost of borrowing than the rate itself.
