Effective Interest Rate Formula
The effective interest rate (EAR) is the actual annual rate you earn or pay after accounting for compounding frequency. It's always higher than the stated nominal rate.
Effective Annual Rate
EAR = (1 + r/n)^n - 1
Where:
- EAR = Effective annual rate
- r = Nominal (stated) annual rate
- n = Number of compounding periods per year
Step-by-Step:
- 1
Find nominal rate
The stated annual interest rate.
- 2
Identify compounding frequency
Monthly (n=12), quarterly (n=4), daily (n=365).
- 3
Apply formula
(1 + r/n)^n - 1 gives the true annual rate.
Worked Examples:
Credit card rate
Nominal: 36% p.a.Compounding: Monthly
Result: EAR = 42.6%
(1 + 0.36/12)^12 - 1 = (1.03)^12 - 1 = 42.6%. The true cost is 42.6%, not 36%!