Question

Two credit cards both state an APR of 20%. First National Bank’s card charges 1.667% compounded monthly. First United Bank’s card charges 10% compounded semiannually (twice a year). Given these APR’s, what are the effective annual rates charged by these two credit cards?

Answer 1

The effective annual rate for the First National Bank card is approximately 21.94%, while for the First United Bank card it is 21%. The EAR tells us the actual interest borrowers will pay, which is higher than the stated APR due to the compounding effect.

Step-by-step explanation:

The student is asking about calculating the effective annual rates (EAR) for two different credit card interest scenarios with the same Annual Percentage Rate (APR) of 20%. For the first card from First National Bank, the interest is compounded monthly at a rate of 1.667%. An EAR calculation for this would be ((1 + 0.01667)^12 - 1) which equals approximately 21.94%. The second card from First United Bank compounds interest semiannually at 10%. The EAR for this would be ((1 + 0.10)^2 - 1), which equals 21%. Both banks, particularly national ones, can match these rates, but the actual cost to the borrower is more accurately reflected in the EAR rather than the advertised APR.