As a college student, you probably receive many credit card offers in the mail. Consider these two offers. The first card charges a 17 percent APR. An examination of the footnotes reveals that this card compounds monthly. The second credit card charges 16.25 percent APR and compounds weekly. What is the effective annual rate of the cheaper card?

Due to poor spending habits, Bryant has accumulated $5,000 in credit card debt. He has missed several payments and now the annual interest rate on the card is 16.75 percent! If he pays $200 per month on the card, in total, how much interest expense does Bryant pay to the credit card company?

847

To calculate the effective annual rate (EAR) of a credit card, we need to take into account the compounding frequency and interest rate. The formula for calculating EAR is:

EAR = (1 + r/n)^n - 1

Where:
r = annual nominal interest rate (APR)
n = number of compounding periods per year

In this case, we have two credit cards with different compounding frequencies and interest rates.

For the first credit card with a 17% APR and monthly compounding, we need to convert the APR to a monthly interest rate. Since compounding is done monthly, there are 12 compounding periods in a year (n = 12).

Monthly interest rate = 17% / 12 = 0.17 / 12 = 0.0142

Now, we can calculate the EAR for this credit card:

EAR1 = (1 + 0.0142)^12 - 1

For the second credit card with a 16.25% APR and weekly compounding, we need to convert the APR to a weekly interest rate. Since compounding is done weekly, there are 52 compounding periods in a year (n = 52).

Weekly interest rate = 16.25% / 52 = 0.1625 / 52 = 0.003125

Now, we can calculate the EAR for this credit card:

EAR2 = (1 + 0.003125)^52 - 1

By calculating the EAR for both credit cards, we can compare which one is cheaper in terms of the effective interest rate.