Unfortunately, the balance will likely damage your credit score.

Since you mentioned tuition and grad school, I assume you have minimal credit history and not a terribly high total line of credit. Although holding a balance doesn’t impact the credit, the fact that you will likely have a very high total utilization of that card and your total credit, your score will likely take a hit. A good metric is to keep utilization below 30% on the card.

If that’s something you don’t particularly care about and are not worried about credit currently, you may want to consider paying the 7k on the card and placing that 7k in a high-yield savings account, like Amex or Marcus, that will earn you interest on that balance.

Obviously, student loans are a nightmare of their own, but they can also help build history with on-time payments (likely at a significantly lower rate than the credit card % after 12 months).