That depends in large part of what you hope to get out of transferring?
What is the “issue” with your current college, that you feel you have to transfer out, even if it means financial burdens for yourself and your family?
What is it that you feel you will gain by attending Barnard? There may be many valid, and good reasons, but not all of them will “calculate” equally well, if you try to “cost-justify” it.