Final answer:
To compare the effective interest rates of the two credit cards, we need to consider the compounding period and the APR of each card. Company A offers a credit card with a 22% APR and monthly compounding, while Company B offers a credit card with a 24% APR and semi-annual compounding. By using the formula for calculating effective interest rate, we can determine that Company B offers the card with the lower effective interest rate.
Step-by-step explanation:
To compare the effective interest rates of the two credit cards, we need to consider the compounding period and the APR of each card. The effective interest rate represents the true cost of borrowing, taking into account the compounding frequency. To calculate the effective interest rate, we can use the formula:
Effective Interest Rate = (1 + (APR / n))^n - 1
Where APR is the annual percentage rate and n is the number of compounding periods per year.
For Company A, which has a 22% APR and monthly compounding, the effective interest rate is: (1 + (0.22 / 12))^12 - 1 = 0.2489, or 24.89%.
For Company B, which has a 24% APR and semi-annual compounding, the effective interest rate is: (1 + (0.24 / 2))^2 - 1 = 0.2456, or 24.56%.