As a college student, you probably receive many credit card offers in the mail. Consider these two offers. The first card charges a 17% APR. An examination of the footnotes reveals that this card compounds daily (365 day year). The second credit card charges 18% APR and compounds semiannually. What is the effective annual rate of the cheaper card?
A) 18.00%
B) 17.00%
C) 18.81%
D) 18.53%

Question

Quizplus · Accepted Answer

To find the effective annual rate of the cheaper card, we need to use the formula:

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

Where APR is the annual percentage rate, and n is the number of times the interest is compounded in a year.

For the first card, we have:

EAR = (1 + 0.17/365)^365 - 1 = 0.1795 or 17.95%

For the second card, we have:

EAR = (1 + 0.18/2)^2 - 1 = 0.1853 or 18.53%

Therefore, the second card has a higher effective annual rate, even though it has a slightly higher APR. So the best choice is to opt for the first card (if there are no other factors to consider).

As a College Student, You Probably Receive Many Credit Card