I'm working on a finance class related problem, concerning the Effective Annual Rate (EAR) of an invoice credit rate.

The standard formula of the EAR is:

$ EAR = \big(1 + \frac{APR}{m}\big)^{m}-1$

where $APR$ is the Annual Percentage Rate and $ m $ is the number of compounding periods.

The cost of delaying payment on the invoice is $ 0.0526\ (5.26\%) $ per 20 days.

I know that the answer is supposed to be:

$ EAR = \big(1 + 0.0526\big)^{\frac{365}{20}}-1 = 1.5487 \approx 155\%$

As you can see, using the standard formula above, would yield another result:

$ EAR = \big(1 + \frac{0.0526}{365/20}\big)^{\frac{365}{20}}-1 = 0.0526 \approx 5.26\%$

My question: why is there no $ m $ denominator in the parenthesis of the suggested solution?

I'm new to this subject so I'm sure the reason for the divergence between the standard formula and the solution is blatantly obvious – probably having to do with the periodization of the EAR (20 days vs. annual rate)? However, I can't seem to grasp the concept properly.


Since "the cost of delaying payment on the invoice is 0.0526 (5.26%) 0.0526 (5.26%) per 20 days" there is no need to divide by anything to get the rate for the compounding period because it is given: 0.0526.

The literal APR (as an annual rate) would be a nominal rate of 95.995 % compounded every twenty days.

m = 365/20 = 18.25
periodic rate = 0.95995/m = 0.0526

Nominal annual rates are defined as the periodic rate * number of periods per year. It is necessary to specify the compounding period when describing a nominal annual rate. For examples see Wiki Calculation.


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