The formula
- d
- Daily rate as a decimal
- B
- 360, 365, or 366
- EAR
- Effective annual rate
- n
- Compounding days per year
Example: daily rate of 0.02%
A daily rate of 0.02% is 0.0002 as a decimal. Simple annualization on a 365-day basis gives:
If 0.02% compounds every day, the effective annual rate is:
Simple annual rate
Use daily rate × 365 when the daily rate is a simple periodic slice of a nominal annual rate. A 360-day contract would multiply by 360 instead.
Effective annual rate
Use (1 + daily rate)365 − 1 when interest compounds daily and you want the actual one-year growth rate.
Do not mix conventions
If a daily rate came from APR ÷ 365, multiplying it by 365 simply recovers the original nominal APR. Compounding that same daily rate produces an effective annual rate that is higher.
Check the math with a calculator
Enter your own numbers in the matching Power of Interest calculator. The calculator performs the arithmetic while this page explains the formula and assumptions behind it.