Franks credit card has no annual fee, 23.99% interest rate. Switch to new card 16.99% rate. $35 annual fee. How much average balance would frank have to make switching cards worth it?

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

With the new card, he'll have to pay a fixed fee of $35 plus the annual interest:

To make switching cards worth it, both payments will need to be (at least) equal:

Rearranging

Solving

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.

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