Given -
Card A charges: 0% interest for the first year, and then 0.8% interest compounded continuously after that.
Card B charges: 0.7% compounded continuously.
Purchase Amount = $500
Payment Made after = 2.5 Years
To Find -
Which Card to choose and the final amount=?
Step-by-Step Explanation -
To find the total amount of interest compounded continuously we use the formula:
[tex]M\text{ = C}\times e^{(r\times t)}[/tex]
Where,
C = Initial Amount
r = Rate of Interest
t = Time
Now,
Since the total amount you have to pay for the purchase on credit card A is lower, it's the best option.
Putting Values in the formula for card A, we get:
[tex]\begin{gathered} M\text{ = 500}\times e^{(0.8\times1.5)} \\ M\text{ = 506.04} \end{gathered}[/tex]
Final Answer -
Option (c): Card A , $506.04
