APY Formula & Calculation

The Annual Percentage Yield (APY) formula calculates the effective annual interest rate based on the nominal interest rate (APR) and the compounding frequency.

The Formula

Where:

• r = The nominal annual interest rate (APR) in decimal form (e.g., 5% = 0.05)
• n = The number of times interest is compounded per year

Step-by-Step Calculation Example

Let's say you have an investment with an APR of 5% that compounds monthly.

1. Convert APR to decimal:
   r = 5% = 0.05
2. Identify compounding frequency:
   Since it's monthly, n = 12
3. Plug values into the formula:
   APY = (1 + 0.05/12)¹² - 1
4. Calculate inside parentheses:
   0.05 / 12 = 0.0041666...
   1 + 0.0041666... = 1.0041666...
5. Raise to power of n:
   (1.0041666...)¹² ≈ 1.05116
6. Subtract 1:
   1.05116 - 1 = 0.05116
7. Convert to percentage:
   0.05116 × 100 = 5.116%

Common Compounding Frequencies