APY vs APR is the difference between the rate a bank states and the rate you actually earn or pay over a year. APR (annual percentage rate) is the simple annual rate before compounding. APY (annual percentage yield) is the effective annual rate after compounding is included. When you compare savings accounts, money market accounts or CDs, APY is the number that tells you what you will actually earn, which is why our CD calculator takes APY as its input. This guide explains both terms, gives the exact conversion formulas, and shows when the difference is big enough to matter.
Definitions in plain English
- APR is the interest rate per year without compounding. If a lender or bank compounds monthly, it divides the APR by 12 and applies that rate each month.
- APY is what that compounding produces over a full year. It is always equal to or higher than the APR, and the gap widens with more frequent compounding and higher rates.
For deposit accounts in the US, the Truth in Savings Act and its rule, Regulation DD, require banks to disclose APY so that accounts with different compounding schedules can be compared on equal terms. For loans and credit cards, lenders disclose APR under the Truth in Lending Act. For mortgages and some other loans, APR also includes certain finance charges and fees, so it is not purely an interest rate. That is a separate concept from the compounding difference covered here.
The conversion formulas
From APR to APY, where n is the number of compounding periods per year:
From APY back to APR:
The second formula is exactly what our CD calculator uses internally to show the nominal rate behind a quoted APY. For continuous compounding, the limit case, APY = e^APR − 1.
Worked example: from APR to APY
Take an example stated rate of 4.5% APR. Here is the APY it produces at each common compounding frequency:
| Compounding | Periods per year | APY from a 4.5% APR |
|---|---|---|
| Annual | 1 | 4.500% |
| Semiannual | 2 | 4.551% |
| Quarterly | 4 | 4.577% |
| Monthly | 12 | 4.594% |
| Daily | 365 | 4.602% |
Going from annual to monthly compounding adds about 0.09 percentage points. Going from monthly to daily adds only about 0.009 points more. On $10,000, that last step is worth roughly $0.85 a year. Daily compounding sounds impressive in marketing, but it is a small improvement over monthly.
Worked example: from APY to APR
Now reverse it. Suppose a bank quotes 4.5% APY. The nominal APR behind it depends on the compounding schedule:
| Compounding | APR that produces 4.5% APY |
|---|---|
| Annual | 4.500% |
| Semiannual | 4.450% |
| Quarterly | 4.426% |
| Monthly | 4.410% |
| Daily | 4.402% |
With daily compounding, the bank only needs a 4.402% APR to deliver 4.5% APY. This is why comparing APYs is the right approach for savings: two banks with the same APY pay the same over a year regardless of how they compound.
What APY means for your balance
Because APY already includes compounding, you can use it directly in a simple growth formula:
Our CD calculator does exactly this. With an example deposit of $10,000 at 4.5% APY:
- After 12 months, the balance is $10,450.00, with $450.00 of interest. Notice that the interest is exactly 4.5% of the deposit, which is the definition of APY.
- After 5 years, the balance is $12,461.82 and total interest is $2,461.82, more than five times the first year's interest because interest earns interest.
At 4.5%, money doubles in about 15.7 years (the Rule of 72 estimate is 16.0). Our guide on Rule of 72 accuracy explains why the shortcut is slightly off at low rates.
The same math on the borrowing side
Credit cards usually quote an APR and charge interest daily or monthly on the balance. The effective annual cost is therefore higher than the APR, just as an account's APY is higher than its APR. As an example, a card with a 24% APR compounding monthly has an effective annual rate of about 26.82%. Card issuers are not required to show this figure, which is one reason high-APR balances grow faster than people expect.
The asymmetry is worth remembering: banks advertise APY on savings because it is the bigger number, and lenders advertise APR on loans because it is the smaller one. Both are legal and accurate; they just answer different questions.
How to compare savings options fairly
- Compare APY to APY. For savings accounts, money market accounts and CDs, ignore the APR and the compounding frequency once you have the APY.
- Check whether the rate is variable. High-yield savings account APYs can change at any time. CD APYs are fixed for the term.
- Factor in the term and access. A CD may pay a higher APY but charges a penalty if you withdraw early. Our guide to CD early withdrawal penalties shows how to calculate that cost.
- Look at minimums and tiers. Some accounts pay the advertised APY only above or below certain balances.
- Think about inflation. A positive APY can still lose purchasing power if inflation runs higher. The inflation calculator shows how much a dollar's value erodes over time.
Where APY matters most
APY matters most when you hold cash for months or years, such as an emergency fund, a house down payment or a CD ladder. For an emergency fund, the emergency fund calculator estimates the interest your target balance would earn at a given APY, and our guide to how much emergency fund you need covers how to size the balance itself. For a ladder of CDs, see how a CD ladder works.
Compounding versus crediting
Two schedules are easy to confuse. Compounding is how often interest is calculated and added to the balance that earns further interest. Crediting is how often that interest appears in your account. A bank can compound daily and credit monthly: it computes interest every day on the growing balance but posts the total once a month. The APY reflects the compounding schedule, provided interest stays in the account. If you withdraw interest as it is credited, you no longer earn interest on it, and your actual return falls toward the APR.
This matters for CDs that offer to pay interest out to a checking account. Taking the interest out is convenient for income, but the APY quoted for the CD assumes the interest stays put. If you have the interest paid out, expect to earn something closer to the APR.
The upper limit: continuous compounding
What if interest compounded every instant? The formula becomes APY = e^APR − 1, where e is about 2.71828. For a 4.5% APR, continuous compounding gives an APY of 4.603%, compared with 4.602% for daily compounding. The difference is in the thousandths of a percent. In other words, daily compounding already captures almost all of the benefit that compounding can provide at a given APR. Continuous compounding appears mostly in finance textbooks and option pricing models, not in bank accounts, but it is useful as a ceiling: no compounding schedule can turn a 4.5% APR into more than 4.603% APY.
APY on terms shorter than a year
APY is an annual measure, but plenty of products run for less than a year. A 6-month CD quoted at 4.5% APY does not pay 4.5% in six months. It pays roughly half a year's worth of growth at that annual rate. Using the same formula as our calculator, a $10,000 deposit in a 6-month CD at 4.5% APY grows to $10,222.52, earning $222.52. That is slightly less than half of the 12-month interest of $450.00, because the second half of a full year would also earn interest on the first half's interest.
The opposite applies to multi-year CDs. A 5-year CD's APY is still an annual figure, and total interest over the term is much larger than five times one year's APY multiplied by the deposit, provided the interest compounds inside the CD.
Promotional and tiered rates
Advertised APYs come with conditions more often than people notice:
- Introductory rates apply for a set period and then reset to a standard rate. Over a full year, your blended return is a mix of both rates, so it is lower than the headline figure.
- Balance tiers pay one APY up to a certain balance and another APY above it. Some accounts pay the high rate only on the first portion of the balance.
- Activity requirements on some checking accounts, such as a minimum number of debit card transactions or a direct deposit, determine whether you receive the advertised APY in a given month.
None of these change the APY math. They change which APY applies to which dollars and months. When an account has conditions, estimate the APY you will actually qualify for, then compare that figure.
Comparing two offers step by step
Suppose you see two example offers. Offer A advertises a 4.4% rate compounded daily. Offer B advertises a 4.42% rate compounded quarterly. Offer B's stated rate is higher, but the compounding differs, so convert both to APY:
| Offer | Stated rate (APR) | Compounding | APY |
|---|---|---|---|
| A | 4.4% | Daily | 4.498% |
| B | 4.42% | Quarterly | 4.494% |
After conversion, Offer A pays more over a year. The gap is 0.004 percentage points, or about $0.42 a year on $10,000. In practice, US banks must state the APY on deposit accounts, so you will rarely need to convert. The exercise shows why the rule matters: without it, a lower stated rate can beat a higher one.
APY and taxes
Interest from bank accounts and CDs is generally taxed as ordinary income in the year it is credited to you, even if it stays in the account. Banks typically send Form 1099-INT when you earn $10 or more of interest in a year. The APY you are quoted is a pre-tax figure. Your after-tax yield depends on your federal and state tax brackets. Interest on US Treasury securities is exempt from state and local income tax, which can make a Treasury yield competitive with a slightly higher bank APY for people in high-tax states. Because tax situations differ, compare the after-tax figure when the difference between two options is small.
Common misunderstandings
"Daily compounding doubles my interest"
No. As the table shows, daily compounding on a 4.5% APR produces only about 0.10 percentage points more than the stated rate. The frequency matters far less than the rate itself.
"APY is the rate I earn each month"
APY is an annual figure. The interest you see each month is roughly the monthly periodic rate (APR ÷ 12) times your balance. Multiply by 12 and you get close to the APR, not the APY; the extra APY comes from interest being added to the balance over the year.
"A higher APR always means more interest"
Only when compounding is the same. A 4.500% APR compounded annually and a 4.402% APR compounded daily both produce 4.5% APY. If one bank quotes APR and another quotes APY, convert one of them before comparing.
"APY includes fees"
For deposit accounts, APY reflects interest and compounding. Monthly maintenance fees are disclosed separately and reduce what you actually keep. If a fee applies to your balance, subtract it from the interest to see your real return.
A quick checklist before you open an account
Before moving money for a higher rate, confirm four things: the APY (not just the rate), whether it is fixed or variable, any balance tiers or activity conditions, and whether the institution is FDIC or NCUA insured. If two accounts are within a few hundredths of a percent, convenience and access usually matter more than the yield difference.
Key takeaways
APR is the stated annual rate; APY is what that rate becomes after compounding. Convert with APY = (1 + APR ÷ n)^n − 1 and APR = n × ((1 + APY)^(1/n) − 1). For savings, compare APY to APY. For borrowing, remember that the effective cost is higher than the APR whenever interest compounds. Use the CD calculator to turn any APY into a dollar balance, and the Rule of 72 calculator to see how long your money takes to double at that rate.
