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# 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%

## Related Topics

• Economics - Engineering economics - cash flow diagrams, present value, discount rates, internal rates of return - IRR, income taxes, inflation.

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