The annual rate of interest that is actually paid or received in a transaction. In other words, it is the actual percent interest that a borrower pays on its loan or that an investor earns on its investment. This rate (known for short as EAR) depends on the nominal rate and the number of compounding periods per year. The effective annual rate reflects the impact of compounding frequency, while the stated annual rate is based on simple interest. The relationship between the two rates is expressed by the following formula:
EAR = (1 + r/m)m– 1
The maximum value of the effective annual rate can attained when the stated annual rate is compounded continuously (c.c). In such a case, the effective annual rate can be calculated by applying the following formula:
EARc.c = er – 1
An example will illustrate the calculation of this rate. Suppose the stated annual rate is 7% and interest is compounded annually, semiannually, quarterly and continuously.
For annual compounding (m= 1):
EAR = (1 + 0.07/1)1– 1= 0.07= 7%
For semiannual compounding (m= 2):
EAR = (1 + 0.07/2)2– 1= 0.071225 = 7.1225%
For quarterly compounding (m= 4):
EAR = (1 + 0.07/4)4– 1= 0.071859= 7.1859%
For continuous compounding (m= ∞):
EARc.c = e0.07 – 1= 0.0725 = 7.25%
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