Answer:
The minimum average balance that makes the switching worth it is $500
Step-by-step explanation:
Equations
We know Frank's credit card has no annual fees and charges an interest rate of 23.99% of his average balance B. He wants to switch to a new card with $35 annual fees but less interest rate of 16.99%.
The total annual payment Frank actually has to pay is given only by the interest of his annual average balance. That is
[tex]P_1=23.99\%\cdot B=0.2399\cdot B[/tex]
With the new card, he'll have to pay a fixed fee of $35 plus the annual interest:
[tex]P_2=35+16.99\%\cdot B=35+0.1699\cdot B[/tex]
To make switching cards worth it, both payments will need to be (at least) equal:
[tex]0.2399\cdot B=35+0.1699\cdot B[/tex]
Rearranging
[tex]0.2399\cdot B-0.1699\cdot B=35[/tex]
[tex]0.07B=35[/tex]
Solving
[tex]B=35/0.07=500[/tex]
[tex]B=\$500[/tex]
The minimum average balance that makes the switching worth it is $500. If his balance is more than $500, he'll save by using the new card.
