About the APY Calculator
This APY calculator converts a nominal annual interest rate (APR) into the annual percentage yield (APY) — the rate you actually earn once interest starts earning interest. Enter the stated rate, how often the bank compounds, and an optional deposit to see the APY, the interest your money earns in one year, and the rate charged each compounding period.
Use it when a bank, credit union or brokerage quotes a rate one way and a competitor quotes it another. US banks must show APY on deposit accounts under the Truth in Savings Act, but loan documents, bond coupons and many international accounts quote a nominal rate, so converting both to APY is the only fair comparison.
The comparison table shows the same APR under every common compounding frequency, so you can see how much (or how little) daily compounding adds over monthly or quarterly. The calculation assumes the rate stays fixed for the full year and no money is withdrawn.
With the default inputs, the apy (annual percentage yield) is 5.116%. Change any value above to recalculate instantly.
How to use the apy calculator
- 1Enter the stated annual interest rate (APR or nominal rate).
- 2Choose how often interest compounds — check the account terms.
- 3Optionally enter a deposit to see what it earns in a year.
- 4Read the APY and compare it with other accounts’ quoted APYs.
- 5Use the table to see how much different compounding frequencies change the yield.
Formula and method
APY expresses one full year of compound growth as a single percentage. The nominal rate r is split into n equal periods; each period the balance grows by r ÷ n, and that growth repeats n times, so the year-end multiplier is (1 + r ÷ n)^n. Subtracting 1 leaves the effective yield.
As n increases the APY rises, but with diminishing returns — the limit is continuous compounding, e^r − 1. One-year earnings are simply deposit × APY, assuming the rate does not change and nothing is withdrawn during the year.
- r
- Nominal annual rate as a decimal (APR ÷ 100)
- n
- Compounding periods per year (365 daily, 12 monthly, 4 quarterly…)
- e
- Euler’s number, ≈ 2.71828
Worked examples
5% compounded monthly on $10,000
Monthly compounding applies 5% ÷ 12 = 0.4167% each month. Twelve months of that growth gives (1.0041667)^12 − 1 = 5.116% APY, so $10,000 earns about $511.62 in a year instead of $500.
4.5% compounded daily on $25,000
Daily compounding at 4.5% gives (1 + 0.045/365)^365 − 1 ≈ 4.6025% APY. A $25,000 deposit earns about $1,150.62 in the first year — roughly $25.62 more than the simple 4.5% would suggest.
6% compounded quarterly vs continuously
Quarterly compounding at 6% applies 1.5% four times: 1.015^4 − 1 = 6.136% APY, so $5,000 earns $306.82. Even continuous compounding would only raise this to 6.184%, showing how quickly the benefit levels off.
Frequently asked questions
What is the difference between APR and APY?+
APR is the nominal yearly rate without compounding. APY includes the effect of interest earning interest during the year, so it is equal to or higher than the APR. Savings accounts in the US advertise APY; loans usually advertise APR.
Is daily compounding much better than monthly?+
Only slightly. At 5%, monthly compounding gives 5.116% APY and daily gives 5.127% — about $1 more per year on $10,000. The rate itself matters far more than the compounding frequency.
How do I convert APY back to APR?+
Reverse the formula: APR = n × ((1 + APY)^(1/n) − 1). For example, a 5% APY with monthly compounding corresponds to an APR of about 4.889%. The interest rate converter does this automatically.
Why do banks advertise APY instead of the interest rate?+
In the US, Regulation DD (the Truth in Savings Act) requires deposit accounts to disclose APY so savers can compare accounts on the same basis regardless of how each bank compounds interest.
Does APY include fees?+
No. APY reflects interest only. Monthly maintenance fees or minimum-balance charges reduce what you actually keep, so an account with a slightly lower APY and no fees can be the better deal.
Results are estimates for educational purposes and are not financial advice. Rates, fees and terms vary — confirm with your lender or a licensed advisor before making decisions.