What Is APY (Effective Annual Yield)?
The Annual Percentage Yield (APY), also called the effective annual yield, is the real rate of return you earn on an investment or savings account in one year once compounding is taken into account. A nominal rate alone hides this effect: 5% compounded monthly actually earns more than a flat 5% paid once a year. This universal financial formula applies anywhere and lets you compare accounts on equal footing.
How to Use This Calculator
Enter the nominal annual interest rate as a percentage (the headline rate a bank quotes), then select how often interest is compounded — annually, semi-annually, quarterly, monthly, weekly, or daily. The calculator returns the effective annual yield, the percentage you truly earn over a year.
The Formula Explained
$$\text{APY} = \left(1 + \frac{i}{n}\right)^{n} - 1$$ where \(i\) is the nominal annual rate written as a decimal and \(n\) is the number of compounding periods per year. Dividing \(i\) by \(n\) gives the rate per period; raising the growth factor to the power \(n\) compounds it across the year; subtracting 1 leaves just the yield. The more frequent the compounding, the higher the APY for the same nominal rate.
Worked Example
Suppose a savings account pays a 5% nominal annual rate compounded monthly. Here \(i = 0.05\) and \(n = 12\). $$\text{APY} = \left(1 + \frac{0.05}{12}\right)^{12} - 1 = (1.0041667)^{12} - 1 \approx 0.051162$$ or about 5.1162%. So your effective return is noticeably higher than the 5% headline rate.
FAQ
What is the difference between APR and APY? APR is the nominal rate without compounding; APY includes the effect of compounding within the year, so \(\text{APY} \geq \text{APR}\).
Does more frequent compounding always help? Yes — for the same nominal rate, daily compounding yields slightly more than monthly, which yields more than annual.
What is the maximum APY? As compounding approaches continuous, APY approaches \(e^{i} - 1\), the upper limit for a given nominal rate.
