Final answer:
The student's question on calculating the Effective Annual Rate (EAR) from an APR of 22.0% with monthly compounding results in an EAR of approximately 24.31%.
Step-by-step explanation:
The student is asking how to calculate the Effective Annual Rate (EAR) given a credit card with an Annual Percentage Rate (APR) of 22.0 percent and monthly compounding of interest.
To calculate EAR, we use the formula: EAR = (1 + (APR/n))^n - 1. Here, APR is the annual percentage rate, and n is the number of compounding periods per year. Since the interest is compounded monthly, n would be 12. We plug the values into the formula as follows:
- APR = 0.22 (or 22% expressed as a decimal)
- n = 12
EAR calculation:
- EAR = (1 + (0.22/12))^12 - 1
- EAR = (1 + 0.0183333)^12 - 1
- EAR = 1.0183333^12 - 1
- EAR = 1.243087 - 1
- EAR = 0.243087 or 24.31%
Therefore, the Effective Annual Rate (EAR) for the credit card is about 24.31%.