Question

A recent college graduate decides to open a credit card in order to pay fortheir upcoming trip across Europe. In order to get a card with a largeenough credit limit to pay for their trip ($5,500), the student agrees to aninterest rate of 38.99% compounded continuously. If no payments aremade for an entire year, what will be the balance on the card rounded tothe nearest cent?

Answer 1

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

`A=P\cdot e^(rt)`

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

`A=5500\cdot e^{(38.99)/(100)\cdot1}=8122.58`

so after one year, the debt would be 8122.58