$$Mary$\text{'}$s credit card situation is out of control because she cannot afford to make her monthly payments. She has three credit cards with the following loan balances and$$ APRs: Card$1,$$$4$ comma $000,21\%$; Card$2,$$$5$ comma $700,25\%$; and Card$3,$$$3$ comma $100,17\%.$ Interest compounds monthly on all loan balances. A credit card loan consolidation company has captured$$ Mary's attention by stating they can save Mary $26\%$ per month on her credit card payments. This company charges $17\mathrm{.}5\%$ APR. Is the$$ company's claim$$ correct? Assume a $10-$year repayment period.