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Effective and nominal interest

Nominal interest is the stated annual rate, while effective interest is the actual annual rate once compounding within the year (and any fees) are included. If interest compounds $m$ times a year, effective interest is higher than nominal, since interest is added more often.

r_{\text{eff}} = \left(1 + \frac{r_{\text{nom}}}{m}\right)^m - 1

effective rate with

m

compounding periods per year

Symbols

$r_{\text{nom}}$	nominal annual rate
$m$	compounding periods per year
$r_{\text{eff}}$	effective annual rate

Example

Nominal rate 5% with monthly compounding ( $m=12$ ):

$r_{\text{eff}} = (1 + 0.05/12)^{12} - 1 \approx 5.12\%$ .

The more compounding periods per year, the bigger the gap between nominal and effective rate.

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Part of Engineering Economics: Interest and time value.