What is the difference between nominal interest rate and the effective annual interest rate?
The nominal interest rate (NIR), is the quoted or stated interest rate (usually per annum) ignoring how frequently interest is compounded.
The effective annual interest rate (EFF) is the equivalent interest rate when interest is compounded once per year. EFF rate will need to be calculated when you’re given an annual interest rate (cost) on a debt item, but are told interest is calculated/compounded more than once per year
EFF = (1 + NIR/m) ^m -1
COMPARE:
i. 8.25% compounded daily
vs
ii. 8.5% compounded annually
- Effective annual rate (EFF) = [1 + 0.0825/365]365 – 1 =8.6% p.a.
- Effective annual rate (EFF) = [1 + 0.085/1]1 – 1 = 8.5% p.a.
Therefore 8.5% compounded annually is cheaper interest than 8.25% compounded daily.