What APY actually tells you about your money
APY (annual percentage yield) is the real return you'll earn on a savings account over one year, including the effect of compound interest. It's different from the interest rate the bank advertises because it accounts for how often interest gets added back into your account and starts earning interest itself.
When a bank tells you the APY, they've already done the compounding math for you. But if you want to verify the number, or compare accounts that compound on different schedules, you need to know how to calculate it yourself. The formula is straightforward, and understanding it shows you exactly why some accounts earn more than others even when their advertised rates look similar.
Key Takeaways
- APY includes compound interest, so it's always equal to or higher than the stated interest rate.
- The formula is APY = (1 + r/n)^n − 1, where r is the annual rate and n is how many times per year interest compounds.
- Daily compounding (365 times per year) earns more than monthly or quarterly compounding at the same rate.
- You can verify a bank's advertised APY by plugging their rate and compounding frequency into the formula yourself.
The formula and what each part means
The APY formula is: APY = (1 + r/n)^n − 1
Here's what each symbol represents:
- r = the annual interest rate (as a decimal). If the bank quotes 4.5%, you use 0.045.
- n = the number of times per year interest compounds. Daily is 365, monthly is 12, quarterly is 4.
- ^n = raise the number in parentheses to the power of n (multiply it by itself n times).
The formula works because each time interest compounds, you earn interest on the interest that was already added. The more often it compounds, the more you earn.
Working through a real example
Suppose you have a savings account with a 4.5% annual interest rate that compounds daily (365 times per year). Here's the calculation:
APY = (1 + 0.045/365)^365 − 1 APY = (1 + 0.000123288)^365 − 1 APY = (1.000123288)^365 − 1 APY = 1.04596 − 1 APY = 0.04596, or 4.596%
Notice that the APY (4.596%) is higher than the stated rate (4.5%). That difference comes entirely from daily compounding. If the same account compounded monthly instead, the APY would be 4.591%. The difference is small, but it compounds over years.
Why compounding frequency matters
Two accounts with the same 4.5% rate will produce different APYs depending on how often interest compounds. Here's how the same 4.5% rate performs under different schedules:
| Compounding Schedule | Times Per Year (n) | APY |
|---|---|---|
| Annually | 1 | 4.500% |
| Quarterly | 4 | 4.586% |
| Monthly | 12 | 4.591% |
| Daily | 365 | 4.596% |
The differences look tiny, but on a $10,000 balance over five years, daily compounding earns roughly $50 more than annual compounding at the same rate. Most online savings accounts compound daily, which is why they often advertise both the rate and the APY separately.
How to use APY to compare accounts
When you're comparing savings accounts, always compare APYs, not rates. The APY is what you'll actually earn. If one bank offers 4.5% APY and another offers 4.45% APY, the first one will earn you more money, regardless of how often each compounds.
Banks are required to disclose APY on deposit accounts, so you should see it clearly on their website or in account disclosures. If you only see an interest rate and no APY, you can calculate the APY yourself using the formula above, or you can ask the bank directly. They must provide it.
One more note: APY assumes you don't withdraw money during the year. If you make withdrawals, the actual interest you earn will be lower because you're earning on a smaller balance for part of the year.
What happens if you know the APY but need the rate
Sometimes you'll see an APY advertised and want to know what the underlying interest rate is. The reverse formula is more complex, but you can work backwards by testing rates in the APY formula until you match the advertised APY.
In practice, you don't usually need to do this. Banks always disclose both the rate and the APY. But if you're reading an older document or a comparison that only lists APY, you now know that the APY is the number that matters for your actual earnings.
Frequently Asked Questions
Is APY the same as the interest rate?
No. The interest rate is what the bank pays you per year. APY is the total return you earn after accounting for compound interest. APY is always equal to or higher than the rate, depending on how often interest compounds.
Why do some accounts show both a rate and an APY?
Banks are required to disclose APY so you can compare accounts fairly. The rate alone doesn't tell you what you'll actually earn because it doesn't account for compounding. Showing both gives you the full picture.
Does APY change if I withdraw money?
APY is a theoretical annual return based on keeping your money in the account for a full year. If you withdraw money, you earn interest only on the balance that remains, so your actual earnings will be lower than the APY suggests.
Can I calculate APY on a checking account?
Yes, the formula works the same way. Most checking accounts earn little or no interest, so the APY is usually 0% or very close to it. Some high-yield checking accounts do pay interest, and you can calculate their APY using the same method.
What if a bank compounds continuously instead of daily?
Continuous compounding uses a different formula involving the mathematical constant e, and it produces a slightly higher APY than daily compounding. In practice, almost no consumer savings accounts use continuous compounding—daily is the standard for high-yield accounts.