We will assume that the total of the trip is paid with the credit card. Recall that the amount after t years, when the rate is compounded continously would be
[tex]A=P\cdot e^{rt}[/tex]where P is the principal, r is the rate and t is the amount of years.
In this case, we have r=38.99%, t =1 and P=5500. So we have that the amount of debt after one year would be
[tex]A=5500\cdot e^{\frac{38.99}{100}\cdot1}=8122.58[/tex]so after one year, the debt would be 8122.58
