Question

For a positive stated annual interest rate and multiple (more than one) compounding periods per year, the EAR is always _________ the APR.

1) greater than
2) less than
3) equal to
4) not related to

Answer 1

The EAR is always less than the APR when there are multiple compounding periods per year.

Step-by-step explanation:

The correct answer is 2) less than.

The EAR (Effective Annual Rate) is always less than the APR (Annual Percentage Rate) when there are multiple compounding periods per year.

To understand why, consider the compounding formula A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount, r is the annual interest rate, n is the number of compounding periods per year, and t is the number of years.

When there are more compounding periods per year, each period is shorter and the interest is added more frequently. This results in a higher growth rate and a higher EAR compared to the APR.

For example, let's say the APR is 5% and there are 4 compounding periods per year. Plugging in the values, we get A = P(1 + 0.05/4)^(4t). If we calculate the EAR for different values of t, we will always find that the EAR is greater than 5%.

Therefore, the EAR is always less than the APR when there are multiple compounding periods per year.