Annual Percentage Yield (APY)

The effective annual rate of return earned on a deposit or investment taking into account intra-year compounding frequencies.

Interactive Calculation Model

Calculate Annual Percentage Yield (APY) in Real Time

Use our verified, free in-browser Compound Interest Calculator to run scenarios and export PDF reports.

Open Calculator

Concept Overview & Principles

While the nominal Annual Percentage Rate (APR) states the raw annualized interest rate, APY reflects the true compound yield received after factoring in monthly, daily, or continuous compounding.

Because accumulated interest earns interest throughout the year, APY is always higher than nominal APR whenever interest compounds more than once annually.

Mathematical Formula

\text{APY} = \left(1 + \frac{r}{n}\right)^n - 1

Calculates true effective yield from nominal rate (r) and compounding frequency (n).

Variable Definitions

APY(Annual Percentage Yield):

Effective annual return in decimal format.

r(Nominal APR):

Stated annual percentage rate in decimal.

n(Compounding Periods):

Number of compounding periods per calendar year.

Step-by-Step Worked Example

Scenario: Comparing a 6% APR compounded monthly vs daily

1Monthly Compounding (n=12): APY = (1 + 0.06/12)^12 - 1 = (1.005)^12 - 1 = 6.168%.

2Daily Compounding (n=365): APY = (1 + 0.06/365)^365 - 1 = 6.183%.

Effective APY is 6.17% (monthly) and 6.18% (daily).

Related Mathematical & Financial Terms

Compound Interest Rule of 72

Loading NexProTools...

Preparing interactive calculation engine

finance