Question

Two credit cards both state an APR of 14%. First National Bank’s card charges 1.1667% compounded monthly. First United Bank’s card charges 7% 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 (EAR) for First National Bank's credit card, which compounds monthly, is approximately 14.93%, while the EAR for First United Bank's credit card, which compounds semiannually, is approximately 14.49%.

Step-by-step explanation:

To calculate the effective annual rate (EAR) for credit cards, we use the formula EAR = (1 + i/n)n - 1, where i is the annual percentage rate (APR) and n is the number of compounding periods per year.

For First National Bank, with an APR of 14% or 0.14 and monthly compounding (n=12), the EAR is (1 + 0.14/12)12 - 1 = (1 + 0.011667)12 - 1.
Calculating this, we find the EAR is approximately 14.93%.

For First United Bank, with an APR of 14% or 0.14 and semiannual compounding (n=2), the EAR is (1 + 0.14/2)2 - 1 = (1 + 0.07)2 - 1.
Calculating this, we find the EAR is approximately 14.49%.

Despite both banks advertising an APR of 14%, due to the differences in compounding frequency, their EARs are different, with the First National Bank charging a slightly higher effective rate due to monthly compounding compared to the semiannual compounding of First United Bank.