Free and instant — plug in your own numbers.
APR (annual percentage rate) is a stated yearly rate that ignores compounding. APY (annual percentage yield) is what you actually earn in a year once interest starts earning interest. When a savings account compounds more than once a year, the APY is always a little higher than the stated rate.
For savings, compare accounts by APY, because it already folds in how often interest is added. For borrowing, the picture flips: the APR you are quoted is usually lower than what an unpaid balance really costs you. The rest of this guide shows the math, a worked comparison, and the traps that make a headline rate look better than it is.
The short version
| APR (or "interest rate") | APY | |
|---|---|---|
| What it measures | The nominal yearly rate | The real yearly return, including compounding |
| Includes compounding? | No | Yes |
| Where you see it | Loans, credit cards, some savings disclosures | Savings accounts, CDs, money market accounts |
| Which is higher? | Lower, or equal with yearly compounding | Higher, or equal with yearly compounding |
On US savings products you will often see the nominal rate labeled "interest rate" rather than APR. It is the same idea: the rate before compounding.
The APY formula
To turn a nominal rate into an APY, you need the rate and the number of times interest is added per year.
Take a 4% rate compounded monthly. Each month you earn 4% ÷ 12 = 0.3333%. Over 12 months that grows to (1.003333)^12 − 1 = 4.07%. The extra 0.07% is interest earned on interest you were paid earlier in the year.
Here is how much the compounding frequency adds at three illustrative rates:
| Stated rate | Annually | Quarterly | Monthly | Daily |
|---|---|---|---|---|
| 2% | 2.00% | 2.02% | 2.02% | 2.02% |
| 4% | 4.00% | 4.06% | 4.07% | 4.08% |
| 6% | 6.00% | 6.14% | 6.17% | 6.18% |
Two things stand out. First, the gap grows as the rate rises. Second, moving from monthly to daily compounding barely matters. In dollars, $20,000 at 4% for one year earns $800.00 with yearly compounding, $812.08 quarterly, $814.83 monthly and $816.17 daily. For a deeper look at that last step, see daily vs monthly compounding.
Key idea APY answers one question: if I leave this money and its interest alone for a year at this rate, how much will it grow? That makes it the fairest single number for comparing savings accounts.
Worked example: the lower rate that pays more
Say you have $15,000 to deposit and two offers:
- Account A: 4.40% interest rate, compounded daily.
- Account B: 4.45% interest rate, compounded once a year.
Account B has the bigger headline number. But convert both to APY:
- Account A: (1 + 0.044 ÷ 365)^365 − 1 = 4.50% APY
- Account B: compounded once a year, so its APY is simply 4.45%
| Account A | Account B | |
|---|---|---|
| Stated rate | 4.40% | 4.45% |
| Compounding | Daily | Annually |
| APY | 4.50% | 4.45% |
| Balance after 1 year | $15,674.69 | $15,667.50 |
| Balance after 3 years | $17,116.49 | $17,092.93 |
The account with the lower stated rate earns $7.19 more in the first year and $23.56 more over three years, assuming both rates stay the same. The amounts are small, which is the honest lesson: compounding frequency is a tiebreaker. A difference of half a percentage point in APY matters far more than whether interest is added daily or monthly.
You can test your own balances in the compound interest calculator. Enter the stated rate, pick the compounding option, and it shows the effective annual yield next to the final balance.
Going the other way: from APY to the stated rate
Sometimes you only see an APY and want the rate behind it, for example to check a bank's monthly interest figure. Rearrange the formula:
A 4.60% APY compounded monthly works out to a stated rate of 4.51%. Compounded daily, the same APY comes from a stated rate of 4.50%. If your monthly statement shows interest that doesn't match what you expect, run this check before calling the bank. A balance that changed during the month is the usual reason the figures differ.
Why your savings rate still isn't what it seems
APY is a better number than the stated rate, but it has limits of its own. These are the gaps that catch people out.
1. APY is a snapshot of a variable rate
Most savings accounts have variable rates. The APY on the day you open the account assumes the rate holds for a full year. If the bank cuts the rate in month three, your actual yield for the year will be lower than the APY you signed up for. A CD (certificate of deposit) locks the rate for its term, which is one of the main trade-offs covered in high-yield savings vs CD.
2. Introductory and tiered rates
A promotional rate may apply only for the first few months, or only to balances up to a cap. Some accounts pay the advertised APY on the first few thousand dollars and a much lower rate on the rest. Read the rate table, not just the banner, and work out the blended yield on the balance you actually plan to keep.
3. Fees can wipe out most of the yield
APY doesn't account for account fees. Suppose you keep $3,000 in an account paying 4.00% APY with a $5 monthly maintenance fee:
| Amount | |
|---|---|
| Interest for the year | $120.00 |
| Fees for the year (12 × $5) | $60.00 |
| Net earnings | $60.00 |
| Effective yield after fees | 2.00% |
Half the yield is gone. On a smaller balance the fee could exceed the interest entirely. Check whether the fee is waived above a minimum balance, and whether you can keep that minimum without strain.
4. Inflation and tax come next
APY is a nominal return. If prices rise by a similar amount over the year, your buying power barely moves, and in many countries the interest is also taxable. The inflation and savings guide shows how to work out your real return after both.
APR on loans and credit cards
The same math works against you when you borrow. In the US, a credit card APR is a nominal rate. Card issuers typically calculate interest using a daily rate, so a balance you carry from month to month compounds.
At an illustrative 24% APR:
- Compounded monthly, the effective annual rate is 26.82%.
- Compounded daily, it is 27.11%.
That is why a balance left unpaid for a year costs more than the APR suggests. The credit card interest guide walks through the daily calculation, and APR vs interest rate explains how loan APRs also fold in certain fees.
The rule of thumb is simple: when you save, the effective rate is above the stated rate (good for you). When you borrow and carry a balance, it is also above the stated rate (bad for you).
US and UK labels
In the US, the Truth in Savings Act requires banks and credit unions to disclose the APY on deposit accounts, so you should always be able to find it. On loans, the Truth in Lending Act governs how APR is disclosed.
In the UK, savings accounts quote the AER (annual equivalent rate), which works the same way as APY. UK APR on borrowing is calculated differently from US APR and already reflects compounding and certain fees, so don't apply the US conversions above to a UK loan quote.
Frequently asked questions
Is a higher APY always better?
For comparing two savings accounts with similar terms, yes. But check fees, minimum balances, rate caps and whether the rate is promotional. A slightly lower APY with no fees and easy access can leave you better off.
Why is my APY the same as the interest rate?
Either the account compounds once a year, or the two figures are so close that they round to the same number. At a 1% rate compounded monthly, for example, the APY is 1.0046%, which shows as 1.00%.
Does APY include deposits I add during the year?
No. APY describes the growth of a balance that sits untouched for a year. If you add money monthly, use a calculator that handles contributions, such as the savings goal calculator, to see when you'll reach a target.
Can a bank change my APY after I open the account?
On a variable-rate savings account, usually yes; the account terms explain how and when. On a CD, the rate is normally fixed until maturity.
A quick checklist before you open an account
- Compare APY, not the stated rate.
- Ask whether the rate is variable, promotional or tiered, and what happens after any intro period.
- List every fee and the balance needed to avoid it.
- Confirm how quickly you can withdraw money and whether there are any limits.
- Run your real balance and monthly deposits through the compound interest calculator to see the difference in dollars, not just percentages.
If the difference between two accounts is only a few dollars a year, choose on convenience, access and fees. If it is a full percentage point or more, the higher APY is usually worth the switch.
This article is for general education and is not financial advice. Rules, rates and products vary by lender and country. See our disclaimer.
