Final answer:
The 8.4% annual interest compounded monthly has a higher APY of approximately 8.9%, compared to the 8.6% interest compounded quarterly, which has an APY of approximately 8.85%. Therefore, option a) is the correct answer.
Step-by-step explanation:
To compare which option has a higher Annual Percentage Yield (APY), we need to calculate the effective annual rate for both interest rates given their compounding periods. For the 8.4% annual interest compounded monthly, the formula to calculate APY is:
APY = (1 + r/n)n - 1
Where r is the annual interest rate (as a decimal) and n is the number of compounding periods per year.
For the 8.4% interest compounded monthly, the APY can be calculated as:
APY = (1 + 0.084/12)12 - 1 = (1 + 0.007)12 - 1 = 1.089 - 1 = 0.089 or 8.9%
Next, for the 8.6% interest compounded quarterly, the APY is calculated the same way:
APY = (1 + 0.086/4)4 - 1 = (1 + 0.0215)4 - 1 = 1.0885 - 1 = 0.0885 or 8.85%
Between the two, 8.4% annual interest compounded monthly has a slightly higher APY.
Therefore, the answer to the question is a) 8.4% annual interest compounded monthly.