Question

You get a new credit card from your bank. The document that comes with the card informs you that the interest rate on that card is 5.4% APR. What is the effective annual rate you'll actually be paying? The credit card company uses monthly compounding of interest. Enter your answer as a percentage, rounded to 2 decimals, and without the percentage sign ('%'). For example, if your answer is 0.23456 , then enter 23.46

Answer 1

The effective annual rate (EAR) for a credit card with a 5.4% APR and monthly compounding is approximately 5.57%.

Step-by-step explanation:

When calculating the effective annual rate (EAR) of a credit card with an annual percentage rate (APR) of 5.4% and with monthly compounding, we need to take into account the effect of compounding interest. The formula to calculate the EAR from the APR given monthly compounding is: EAR = (1 + (APR/n))^n - 1

Where n represents the number of compounding periods per year. In this case, with monthly compounding, n equals 12. Substituting the given APR of 0.054 (5.4% expressed as a decimal) into the equation, we get: EAR = (1 + (0.054/12))^12 - 1 EAR = (1 + 0.0045)^12 - 1 EAR = 1.0045^12 - 1 EAR = 1.055689 - 1 EAR = 0.055689, or about 5.57% when rounded to two decimal places.

Thus, the effective annual rate that the credit card holder will actually be paying is approximately 5.57%.