Effective Interest Rate vs. Nominal Interest Rate

An interest rate is only meaningful in the context of time - in general is understood as - per year - which may be called

• the nominal interest rate

With other periods of time than the year - like month, week, or day - the interest rate may be called 

• the effective interest rate 

Calculating Nominal Interest Rate

Nominal interest rate for a period with effective interest rates in it's sub-periods can be calculated as

i = (1 + i_e)ⁿ - 1            (1)

where

i = nominal interest rate for the period

i_e = effective interest rate for the sub-period

n = number of sub-periods

Example - Nominal interest rate with Effective monthly interest rates

Nominal interest rate (per year) with 12 monthly effective rates of 1% (i_e = 0.01) can be calculated as

i_n = (1 + 0.01)¹² - 1

    =  0.127

    = 12.7%

Calculating Effective Interest Rate

Effective interest rate for sub-periods of a period can be calculated as

i_e = (i_n + 1)^1/n - 1        (2)

Example - Nominal interest rate with Effective monthly interest rates

The effective interest rate per month with a nominal rate of 10% can be calculated as

i_e = (0.1 + 1)^1/12 - 1

    =  0.00797

    = 0.797%

Temperature ^oC
K
^oF

Length m
km
in
ft
yards
miles
naut miles

Area m²
km²
in²
ft²
miles²
acres

Volume m³
liters
in³
ft³
us gal

Weight kg_f
N
lbf

Velocity m/s
km/h
ft/min
ft/s
mph
knots

Pressure Pa
bar
mm H₂O
kg/cm²
psi
inches H₂O

Flow m³/s
m³/h
US gpm
cfm