How to use this APY calculator
- Nominal annual rate, enter the stated yearly interest rate (the APR) as a percentage.
- Compounding frequency, choose how often interest is added: daily, monthly, quarterly, semi-annually or annually.
- Deposit amount, optionally enter a starting balance to see the interest and ending balance in money terms.
- Read your APY, interest in one year and balance after one year, they update instantly as you type.
- Scroll to the compare compounding frequencies table to see how the same nominal rate plays out across annual, semi-annual, quarterly, monthly, daily and continuous compounding.
How APY is calculated
The annual percentage yield converts a nominal rate into the effective return after compounding. The formula is APY = (1 + rate / n)n - 1, where rate is the nominal annual rate written as a decimal and n is the number of compounding periods per year. APY is higher than the nominal rate because of compounding: each time interest is added, the next round of interest is earned on a slightly larger balance, so the more often interest compounds, the more you end up with. When interest compounds just once a year, the APY equals the nominal rate exactly.
A worked example
Suppose you have a nominal annual rate of 5% that compounds monthly, so n is 12. Writing the rate as a decimal gives 0.05, and 0.05 divided by 12 is about 0.004167. Adding 1 and raising to the 12th power gives roughly 1.05116, and subtracting 1 leaves 0.05116, an APY of about 5.116%. On a 1,000.00 deposit that is about 51.16 in interest over the year, for a balance of 1,051.16. The same 5% compounded daily would push the APY to roughly 5.127%, a small but real edge from more frequent compounding.
Comparing compounding frequencies at the same rate
The calculator's comparison table takes the nominal rate and deposit you entered and runs them through six compounding frequencies at once: annually, semi-annually, quarterly, monthly, daily and continuous. Continuous compounding is the theoretical limit where interest is added constantly rather than at fixed intervals, and it works out to APY equals e raised to the rate, minus 1. Lining all six up side by side shows that most of the gain from more frequent compounding happens early, moving from annual to monthly compounding matters far more than moving from daily to continuous, which typically differ by only a few thousandths of a percentage point.
Why APY matters when comparing accounts
Two accounts can advertise the same nominal rate yet pay different amounts if they compound at different frequencies. APY puts everything on a single, comparable basis, which is why it is the figure most savings products are required to quote. When you shop around, compare APY to APY rather than nominal rate to nominal rate.
Note: This calculator is for general information only and is not financial advice. Real accounts may apply fees, tiered rates, introductory bonuses or minimum balances that change the return you actually receive.
Frequently asked questions
What is APY?
APY is the annual percentage yield, the real one-year return on a deposit once compounding is included, so it reflects what you actually earn rather than just the stated nominal rate.
What is the difference between APR and APY?
APR is the nominal annual rate before compounding, while APY folds compounding in. If interest compounds more than once a year the APY is higher, and they are equal only when interest compounds once a year.
Does more frequent compounding give a higher APY?
Yes. For the same nominal rate, daily compounding yields a little more than monthly, which beats quarterly or annual. The extra gain gets smaller as the frequency rises.
What is continuous compounding?
Continuous compounding is the theoretical limit of compounding more and more often, where interest is added constantly instead of at fixed intervals. It works out to APY equals e raised to the nominal rate, minus 1, and it produces only a slightly higher APY than daily compounding at the same rate.