APR vs APY: What the Two Rates Really Tell You
A bank might quote a savings rate of 4.90% on one page and 5.02% on another, and both can be correct. The first is usually an annual percentage rate (APR), a stated yearly rate. The second is an annual percentage yield (APY), which shows what you actually earn in a year once compounding is counted.
Knowing the difference lets you compare two accounts, or two loans, on equal terms. This guide gives the conversion formula, a worked comparison, and the situations where the two numbers matter most.
What each term means
- APR is the nominal yearly rate. It does not show the effect of interest being added to the balance during the year.
- APY is the effective yearly rate. It includes compounding, so it is the percentage your balance really grows over exactly one year. You may also see it called the effective annual rate.
If interest compounds only once a year, APR and APY are equal. The more often interest compounds, the further APY rises above APR. The gap also depends on the size of the rate: it grows roughly with the square of the rate, so it is a few hundredths of a point at 2% and nearly three points at 24%.
APY = (1 + APR/n)^n − 1APR as a decimal, n = compounding periods per year.
One rate, many yields
Take a 5% APR and change only how often it compounds. Each row applies the formula above:
| Compounding | n | APY |
|---|---|---|
| Yearly | 1 | 5.0000% |
| Twice a year | 2 | 5.0625% |
| Quarterly | 4 | 5.0945% |
| Monthly | 12 | 5.1162% |
| Daily | 365 | 5.1267% |
Worked example, monthly: the periodic rate is 0.05 ÷ 12 = 0.0041667. Raised to the 12th power, 1.004166712 = 1.051162, so the APY is 5.1162%. A 1,000 deposit grows to 1,051.16 after one year.
The yield barely moves between monthly and daily compounding. The biggest gap is between not compounding at all and compounding at least a few times a year.
Comparing two savings accounts
Account A quotes 4.90% compounded daily. Account B quotes 4.95% compounded yearly. B has the higher headline number, so it looks better.
Convert both to APY. Account A: (1 + 0.049 ÷ 365)365 − 1 = about 5.02%. Account B: with one compounding period, the APY is simply 4.95%. Account A pays more, even though its quoted rate is lower. On a 10,000 deposit, that is roughly 502 against 495 after one year.
The rule is simple: compare APY with APY, or APR with APR at the same compounding frequency. Never compare one of each.
The gap also builds over time. A 10,000 deposit at a 5% APR compounded monthly grows to 10,000 × (1 + 0.05 ÷ 12)60 = 12,833.59 in five years, against 12,762.82 with yearly compounding. That is 70.77 more from the same quoted rate, and the difference grows with bigger balances and longer terms.
Borrowing, and converting back
For borrowers the same maths works against you. A card that charges 24% APR with interest added monthly applies 2% each month, so the effective yearly cost is 1.0212 − 1 = 26.82% on a balance you do not pay down. A lower stated APR with more frequent compounding can cost more than a slightly higher APR with less frequent compounding.
To go the other way, from a known APY to the matching APR, use:
APR = n × ((1 + APY)^(1/n) − 1)
For example, a 5% APY with monthly compounding corresponds to an APR of 12 × (1.051/12 − 1) = 4.8889%.
Naming and rules differ by country and product. In the United States, for instance, deposit accounts advertise an APY, while loan APRs can also include certain fees, so a loan APR is not always a pure interest rate. Check how the provider defines its figure.
A quick checklist
- Find out whether a quoted number is APR or APY before comparing anything.
- For savings, a higher APY is better; for borrowing, a lower APR (with the same fees and terms) is better.
- Check how often interest compounds and whether it is credited to the balance.
- Remember that neither number includes tax, and neither guarantees a future rate if the rate is variable.
To convert quickly, use the APY calculator. To see what the rate does to a balance over several years, try the compound interest calculator. For the effect of compounding alone, read does compounding frequency matter?.
This article is general education, not financial advice. Rates and the way they are disclosed change, so rely on the provider's own terms for any real decision.
- APY Calculator: Enter the stated interest rate and how often it compounds to get the annual percentage yield. Add a starting balance and a term to see the interest it earns.
- Compound Interest Calculator: Enter a starting balance, an interest rate and a term to see how money grows when interest is added to the balance. Add regular deposits or withdrawals to model a savings plan.
This article is general information, not professional advice. See our Disclaimer and Editorial Policy.
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