Question

American Express and other credit card issuers must by law print the Annual Percentage Rate (APR) on their monthly statements. If the APR is stated to be 18.00%, with interest paid monthly, what is the card's EFF%?

a.22.65%
b.19.56%
c.18.58%
d.20.54%
e.21.57%

Answer 1

The card's Effective Annual Rate (EFF%) given an Annual Percentage Rate (APR) of 18.00% with monthly compounding is 19.56%, which corresponds to option b.

Step-by-step explanation:

To calculate the Effective Annual Rate (EFF%) when given an Annual Percentage Rate (APR) of 18.00% with monthly compounding, we can use the following formula:

EFF% = (1 + APR/n)^n - 1

Where APR is the annual percentage rate and n is the number of compounding periods per year. In this case, interest is compounded monthly, so n = 12.

Therefore, the calculation is as follows:

EFF% = (1 + 0.18/12)^12 - 1

EFF% = (1 + 0.015)^12 - 1

EFF% = (1.015)^12 - 1

EFF% = 1.1956 - 1

EFF% = 0.1956, or 19.56%

So the card's EFF% is 19.56%, which corresponds to option b. This represents the actual annual rate charged when taking into consideration the effects of compounding interest throughout the year.