Investment
Nominal rate versus effective annual rate
The effective annual rate is the one-year accumulation rate after accounting for every compounding period within that year.
Definition
The effective annual rate is the one-year accumulation rate after accounting for every compounding period within that year.
Intuition
The nominal rate is divided into periodic rates; interest earned early can earn more interest, so EAR usually exceeds a positive nominal rate.
Formula
EAR is the annual compound factor minus one; daily compounding uses 365 periods.
Formula variables
r is the nominal annual rate and m is compounding periods per year. This tool supports 1, 2, 4, 12, or 365 periods; daily compounding uses a fixed 365-day year.
When to use it
Use EAR to compare deposits or loans with the same quoted nominal rate but different compounding frequencies. It covers compounding only, not fees or other cash flows.
Example
- Enter a 12% nominal annual rate and monthly compounding (12 periods per year).
- The periodic rate is 12% ÷ 12 = 1%; the annual factor is 1.01¹².
- EAR is about 12.68%, roughly 0.68 percentage points above the nominal 12%.
Common mistakes
Do not confuse EAR with CAGR or compare nominal rates alone when compounding conventions or fees differ.
Frequently asked questions
Is EAR the same as CAGR?
No. EAR derives a one-year effective rate from a nominal rate and frequency; CAGR derives an annualized rate from beginning and ending values over a period.
What if compounding is annual?
With one compounding period per year, EAR equals the nominal annual rate.
How many days does daily compounding use?
This calculator uses exactly 365 equal compounding periods per year; leap years do not change that convention.