# Interest Rates - Effective and Nominal

## The relation between effective and nominal interest rates

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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 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 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

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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