Final answer:
To find the actual rate of interest (EAR) with a quoted APR of 16.7% compounded monthly, you use the EAR formula which calculates to approximately 18.38%. This rate is higher than the stated APR due to the effects of monthly compounding.
Step-by-step explanation:
To calculate the actual rate of interest (EAR) that you are paying on a credit card with a quoted annual percentage rate (APR) of 16.7%, where interest is billed monthly, you can use the following formula:
EAR = (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, since the interest is compounded monthly, n equals 12. Plugging the numbers into the formula, we get:
EAR = (1 + (0.167/12))^12 - 1
This gives us:
EAR = (1 + 0.013917)^12 - 1
EAR = 1.018384 - 1
EAR = 0.018384
After converting this decimal to a percentage, the EAR is approximately 18.38%.
It's clear that the actual rate of interest paid, known as the effective annual rate (EAR), is higher than the stated APR due to monthly compounding. Credit card users should be mindful of this when considering the cost of borrowing using credit cards as a financial instrument.