Final answer:
The annual interest rate for an account that compounds interest quarterly with an APY of 4.3% can be calculated using the conversion formula for compounded interest. Upon solving, the annual interest rate comes out to be 4.23%.
Step-by-step explanation:
The question is asking to find the annual interest rate of an account that compounds interest quarterly with an annual percentage yield (APY) of 4.3%. To find the annual interest rate, you will need to understand the relationship between APY and the nominal interest rate when compounding quarterly.
An APY reflects the total amount of interest paid on an account, based on the interest rate and the number of times that interest is compounded per year. The formula for converting APY to the nominal annual interest rate when interest is compounded quarterly is:
APY = (1 + (nominal rate / 4))^4 - 1
We can rearrange this formula to solve for the nominal annual interest rate:
nominal rate = 4 * [(1 + APY)^(1/4) - 1]
Substituting 4.3% or 0.043 for APY, we get:
nominal rate = 4 * [(1 + 0.043)^(1/4) - 1]
nominal rate = 4 * [(1.043)^(1/4) - 1]
nominal rate = 4 * [(1.01058) - 1]
nominal rate = 4 * 0.01058
nominal rate = 0.04232 or 4.23%
Therefore, the annual interest rate for the account, when compounded quarterly, is 4.23%.