Key Takeaways
Direct answer: The interest rate is the simple, uncompounded annual rate a bank states; APY is the actual return earned over a year once compounding is included, and it is always equal to or higher than the stated rate. Because compounding frequency differs between accounts, APY, not the interest rate, is the correct number for comparing deposit products against each other.
- APY equals (1 + r/n)^n − 1, where r is the nominal annual interest rate and n is the number of compounding periods per year.
- More frequent compounding, daily instead of monthly, produces a higher APY for the same stated interest rate, because interest starts earning interest sooner.
- A 5% nominal rate compounds to about a 5.116% APY monthly and about a 5.127% APY daily, a small but real and mathematically consistent difference.
- The Truth in Savings Act requires banks to disclose APY specifically so consumers can compare accounts on equal footing.
The Formula
Annual percentage yield is calculated as:
APY = (1 + r/n)^n − 1
where r is the nominal annual interest rate expressed as a decimal and n is the number of times interest compounds per year. When n equals 1, meaning interest compounds only once annually, APY and the stated interest rate are identical. As n increases, monthly, weekly, daily, APY rises above the stated rate, because interest that has already been credited begins earning its own interest before the year is over. The gap between APY and the stated rate grows with both the compounding frequency and the size of the rate itself, though the effect is modest at the interest-rate levels typical of bank deposit accounts.
Worked Example: 5% Compounded Monthly vs. Daily
Consider a 5% nominal annual interest rate offered by two different accounts, one that compounds monthly and one that compounds daily.
Monthly compounding (n = 12): APY = (1 + 0.05/12)^12 − 1 = (1.0041667)^12 − 1 ≈ 5.116%.
Daily compounding (n = 365): APY = (1 + 0.05/365)^365 − 1 = (1.0001370)^365 − 1 ≈ 5.127%.
On a $10,000 balance held for a full year, the monthly-compounding account would credit approximately $511.60 in interest, while the daily-compounding account would credit approximately $512.70, a difference of about $1.10. The gap is small in dollar terms at this balance and rate, but it grows with larger balances, higher rates, and longer holding periods, and it is entirely mechanical: two accounts advertising the same 5% rate are not paying the same amount unless they also compound on the same schedule.
Change the compounding frequency and watch the effective yield move. The same calculation as the full APY / Effective Yield Calculator, which also shows the nominal-rate summary and is linked below.
Calculate APY From a Nominal Rate
Effective annual yield
- APY
- 5.1162%
- Balance after one year
- $10,511.62
- Interest earned
- $511.62
APY = (1 + r/n)^n − 1. A single-year projection at a constant rate, with no deposits or withdrawals. Educational only, not a rate quote or a recommendation.
Full tool, with the nominal-rate and frequency summary: APY / Effective Yield Calculator.
Why It Matters When Comparing Accounts
A bank can advertise a stated interest rate that looks competitive while compounding less frequently than a rival offering a slightly lower rate with more frequent compounding, and the two can end up paying nearly the same real return, or the opposite of what the headline rates suggest. Comparing accounts on APY removes this ambiguity, because APY is defined to already reflect each account's actual compounding schedule.
The Truth in Savings Act, implemented through the Consumer Financial Protection Bureau's Regulation DD, requires banks to disclose APY for deposit accounts precisely so that a consumer does not need to know each institution's compounding frequency to compare offers. When shopping for a high-yield savings account, CD, or money market deposit account, use the disclosed APY figure, not the stated interest rate, and confirm the APY quoted is current, since rates on variable-rate products change with market conditions.
Frequently Asked Questions
What is the difference between APY and interest rate?
The interest rate is the simple, uncompounded annual rate a bank pays before compounding is taken into account. Annual percentage yield (APY) is the actual return earned over a year once compounding frequency is included, so APY is always equal to or higher than the stated interest rate for the same account. APY, not the interest rate, is the correct figure for comparing accounts against each other.
What is the formula for APY?
APY equals (1 + r/n)^n minus 1, where r is the nominal annual interest rate expressed as a decimal and n is the number of compounding periods per year. A 5% nominal rate compounded monthly (n = 12) produces an APY of about 5.116%, while the same 5% rate compounded daily (n = 365) produces a slightly higher APY of about 5.127%, because more frequent compounding lets interest start earning its own interest sooner.
Why can two accounts with the same interest rate pay different amounts?
Two accounts can advertise the identical stated interest rate but compound on different schedules, daily, monthly, or quarterly, which produces different actual returns. The account that compounds more frequently converts a given nominal rate into a higher APY, because interest already earned begins generating its own interest sooner in the year.
Are banks required to disclose APY?
Yes. The Truth in Savings Act, implemented through Regulation DD, requires banks to disclose the annual percentage yield for deposit accounts such as savings accounts, checking accounts, money market accounts, and CDs, specifically so consumers can compare accounts on a consistent, compounding-adjusted basis rather than relying on the stated interest rate alone.
Is APY the same as APR?
No, and they sit on opposite sides of a transaction. APY describes what a deposit earns, and it includes the effect of compounding. APR describes what borrowing costs, and it is expressed without compounding but folds in certain required fees. A credit card statement showing an APR and a savings account showing an APY are therefore built on different conventions, so the two numbers are not comparable even when they look like the same kind of percentage.
Why does a CD quote both an interest rate and an APY?
The interest rate is the nominal rate applied to the balance, and the APY converts that into what a full year would actually produce given how often the institution credits interest. On a CD whose interest compounds within the term, the APY sits above the stated rate. On one that pays interest out rather than crediting it back, the two can be identical. Disclosure rules require the APY precisely so terms with different compounding can be compared directly.
Does APY assume the balance stays untouched for a full year?
Yes. APY is calculated as though the rate and the balance both hold for twelve months with interest left to compound. A variable-rate account rarely satisfies either assumption: the institution can change the rate at any time, and deposits or withdrawals change the balance the rate applies to. APY is therefore a standardized basis for comparing offers at a point in time rather than a projection of what a specific account will pay.
What is the daily periodic rate shown on a statement?
The daily periodic rate is the nominal annual rate divided by the number of days in the year, and it is the figure a bank applies to each day's balance when interest compounds daily. Multiplying it by the balance gives that day's interest, which is added before the next day is calculated. It is a calculation input rather than a comparison figure, which is why it looks so much smaller than either the stated rate or the APY.
How do you compare a bank APY with a money market fund yield?
They are quoted on different conventions, so a direct comparison overstates one side. A bank APY is a forward-looking annualization that assumes the current rate persists and compounds. A money market fund's seven-day yield annualizes what the fund has just distributed, net of expenses, over a very short backward-looking window. Comparing them fairly means recognizing that the fund figure moves as market rates move while the bank figure holds until the institution changes it.