Is it possible to close an account that has a balance on it and make payments without the finance charges and apr's accruing? In other words, I would like to try to pay off the balance, but can get nowhere with finance and apr's applied. Thanks.

This would be nice, but it is not possible. As long as you have a balance you will be charged monthly finance charges.

If you have a good credit history you may want to transfer the balance to a lower interest credit card or look into a debt consolidation loan.