Final answer:
The compounding period that comes closest to continuous compounding for achieving an Equivalent Annual Rate is one with the highest frequency, such as daily or hourly compounding.
Step-by-step explanation:
The question asks about the compounding period that would provide an Equivalent Annual Rate (EAR) closest to continuous compounding. In the context of finance, continuous compounding is considered the limit case of compounding frequency, and it implies that interest is being calculated and added to the principal an infinite number of times per unit time.
The compounding period that would provide an EAR closest to continuous compounding is the one with the highest frequency of compounding within a year. Mathematically, continuous compounding is represented as the limit of compound interest as the number of compounding periods per year increases indefinitely. Thus, if we are limited by practical, non-continuous options, the more frequent the compounding, such as daily or even hourly, the closer the EAR will be to the rate achieved through continuous compounding.