# Effective Annual Rate (EAR) calculation from periodic rate of invoice credit

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.

m = 365/20 = 18.25