Effective Interest Rate vs. Nominal Interest Rate
Effective interest rate vs. nominal interest rate in sub-periods.
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 + ie)n - 1 (1)
where
i = nominal interest rate for the period
ie = 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% (ie = 0.01) can be calculated as
in = (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
ie = (in + 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
ie = (0.1 + 1)1/12 - 1
= 0.00797
= 0.797%