Final answer:
The statement is false because the effective annual interest rate can be equal to or higher than the annual percentage rate, depending on the compounding frequency.
Step-by-step explanation:
The statement "The effective annual interest rate cannot be less than the annual percentage rate (APR)" is false. The effective annual interest rate (also referred to as EAR or effective interest rate) takes into account the effects of compounding within the year, whereas the annual percentage rate does not consider the compounding effect. For example, if an interest rate is quoted as 6% APR compounded semi-annually, the EAR would be slightly higher because of the compounding effect.
However, the EAR can never be lower than the quoted APR if there is more than one compounding period per year. If interest is compounded annually (once per year), then the EAR is equal to the APR. Therefore, if compounding occurs more frequently, the EAR will exceed the APR, reflecting the additional interest earnings due to compounding.