211.1
1. You receive two credit card offers in the mail on the same day. One charges a rate of 16% compounded monthly while the other charges 16.25% compounded semi-annually. Which is the better card? (1 pt)
The quoted rates from credit cards are the annual percentage rate (APR). The effective annual rate (EAR) depends on the compounding frequency (m) and is given by:
\(EAR = \left (1+\frac{APR}{m} \right )^m - 1 \)
so
\(EAR_1 = \left (1+\frac{.16}{12} \right )^{12} - 1 = 0.172 \) or 17.2%
\(EAR_2 = \left (1+\frac{.1625}{2} \right )^2 - 1 = 0.169 \) or 16.9%
Card 2 has the lower effective annual rate and is a better offer.