Finance
The core distinction
APR stands for Annual Percentage Rate. It is a simple annualized rate: take the periodic interest rate and multiply it up to a yearly figure, ignoring the fact that interest earned or charged partway through the year can itself earn or be charged interest. In other words, APR treats the year as flat and does not account for intra-year compounding.
APY stands for Annual Percentage Yield. It describes the same money but includes compounding, so it reflects the true yearly rate — what you actually end up paying or earning after a full year of interest building on interest. Because of that, APY is always at least as large as the APR it is derived from, and it is larger whenever interest compounds more than once a year.
The shortcut to remember: APR is the quoted rate; APY is the effective rate. If interest only compounded once per year, the two would be identical. The gap between them is entirely the contribution of compounding.
Where you see each one
The two terms tend to live on opposite sides of the financial ledger:
- APR appears on what you borrow. Loans, mortgages, car finance and credit cards are quoted in APR. On a credit card, the issuer also lists a periodic rate, and the APR is just that rate annualized. Importantly, loan APR is also required to fold in certain fees, not just interest.
- APY appears on what you save. Savings accounts, certificates of deposit (CDs) and other interest-bearing deposits are advertised in APY, because it shows the real return after compounding.
APY = (1 + APR/n)^n − 1, where n is the number of compounding periods per year (12 for monthly, 4 for quarterly, 365 for daily). When n = 1, APY equals APR exactly.A worked example
Suppose a product carries a 12% APR compounded monthly. Here n = 12, so the monthly rate is 0.12 ÷ 12 = 1%. Applying the formula:
APY = (1 + 0.12/12)^12 − 1 = (1.01)^12 − 1 ≈ 0.1268
That works out to roughly 12.68% APY. The headline rate was 12%, but once each month's interest starts earning interest of its own, the effective yearly rate climbs by about two-thirds of a percentage point. On a large balance, that gap is real money.
Same rate, different compounding
The more often interest compounds, the bigger the gap between APR and APY. Take a fixed 5% APR and watch the APY rise as compounding gets more frequent:
| Compounding | Periods (n) | APY |
|---|---|---|
| Annually | 1 | 5.000% |
| Quarterly | 4 | 5.095% |
| Monthly | 12 | 5.116% |
| Daily | 365 | 5.127% |
Notice the gains taper off: jumping from annual to monthly adds far more than jumping from monthly to daily. Compounding has a ceiling — even infinitely frequent ("continuous") compounding of 5% only reaches about 5.127%. You can check any of these figures with the APY calculator or model the growth over time with the compound interest calculator.
Why the marketing works the way it does
Because APY is always the higher number, banks advertise APY on savings — it makes the return look as generous as possible. Lenders, wanting the cost to look small, advertise APR on loans. Neither is dishonest; they're just each quoting the figure that flatters their offer. The trap is comparing one product's APR against another's APY, which is never a fair fight.
To compare offers apples-to-apples, convert everything to the same measure. For savings, get every account to APY (or confirm the compounding frequency and convert). For loans, compare APRs that use the same compounding assumptions and the same fee treatment. If you only have an APR and the compounding frequency, the formula above turns it into APY in one step.
A note on loan APR and fees
There's one more wrinkle worth knowing: a loan's APR is usually not the same as its raw interest rate either. Regulations require lenders to bake certain mandatory costs — origination fees, discount points, some closing costs — into the APR and spread them across the term. That's helpful, because it makes APR a truer cost-of-borrowing figure than the bare interest rate. But it also means you shouldn't read a loan's APR as pure interest. When you shop a mortgage or compare a car loan, the APR captures fees that the advertised interest rate leaves out.
The takeaway
APR is the simple, stated rate; APY is what that rate really becomes once compounding is counted. Savings are sold in APY because it looks bigger; loans are quoted in APR because it looks smaller — and loan APR quietly includes some fees on top. Whenever two offers are quoted differently, convert them to the same yardstick before deciding. One formula does the whole job.
Frequently asked questions
- Is APR or APY higher for the same rate?
- APY is always equal to or higher than the APR it is built from, because APY adds the effect of compounding within the year. They are only equal when interest compounds exactly once per year. The more often it compounds, the wider the gap between the two.
- Why do lenders quote APR but banks quote APY?
- Each side quotes the number that looks more attractive. On a loan, APR is the lower figure, so lenders advertise it. On savings, APY is the higher figure, so banks advertise it. Both are describing the same underlying math from opposite directions.
- Does loan APR include fees?
- Often yes. By regulation, loan APR folds in certain required costs such as origination fees and points, spreading them across the term. That makes APR a better cost comparison than the bare interest rate, but it also means a loan APR is not the same as its pure interest rate.
- How do I convert APR to APY?
- Use the formula APY = (1 + APR/n)^n − 1, where n is the number of compounding periods per year. For 12% APR compounded monthly, n is 12, giving (1 + 0.12/12)^12 − 1 = 0.1268, or about 12.68% APY.
This guide is general educational information, not financial advice.