Effective and Nominal Interest Rates

Relationship between effective and nominal interest rates

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 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 for it's subperiods 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 subperiod

n = number of subperiods

Example - Nominal interest rate with Effective monthly interest rates

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

i_n = (1 + 0.010 )¹² - 1

    =  0.127

    = 12.7%

Calculating Effective Interest Rate

Effective interest rate for the subperiods 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

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%

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