Final answer:
A 1-year loan with a 5% APR will have the most interest charged when it is compounded continuously, as this method assumes an infinite number of compounding periods, leading to the highest total interest.
Step-by-step explanation:
The question pertains to the compound interest aspect of loans and investments. In particular, a 1-year loan with a 5% Annual Percentage Rate (APR) will have the most interest charged when it is compounded more frequently. Interest can be compounded in different periods such as annually, semi-annually, quarterly, monthly, daily, or continuously. The more frequent the compounding, the higher the amount of interest that will accumulate over time, given the same nominal interest rate.
Compounding annually means the interest is calculated and added to the principal once a year. However, if we compound semi-annually, for example, the interest is calculated and added to the principal twice a year, resulting in a higher total interest accumulated over the course of a year.
Continuous compounding will always yield the highest total interest because it assumes that interest is being compounded an infinite number of times per year, and thus grows the loan amount as fast as theoretically possible over the given time period.