question 3 (10 points)\nmerle has an offer from a credit card issuer for a 0% apr for the first 60 days and…

Answer:

B. 23.19%

Explanation:

Step1: Calculate the number of days with non - zero rate

There are 365 days in a year. The first 60 days have 0% APR. So the number of days with 21.19% APR is $n = 365 - 60=305$ days.

Step2: Use the effective - interest rate formula

The formula for the effective annual rate (EAR) when compounded daily is $EAR=(1 + \frac{r}{365})^{365}-1$, where $r$ is the annual percentage rate. Here, for the non - zero part, $r = 0.2119$. First, find the growth factor for the 305 - day period with interest. Let $i=\frac{0.2119}{365}$. The value of the account after 305 days of interest - earning and 60 days of non - interest earning is equivalent to $(1 + 0)^{60}\times(1 + i)^{305}$. $(1 + i)^{305}=(1+\frac{0.2119}{365})^{305}$. Let $x=\frac{0.2119}{365}\approx0.000580548$. $(1 + x)^{305}=1.2319$. So the effective interest rate is approximately 23.19%.