Mary'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$$ APRs: Card$1,$$$4000,20\%$; Card$2,$$$5500,23\%$; and Card$3,$$$3100,17\%.$ Interest compounds monthly on all loan balances. A credit card loan consolidation company has captured$$ Mary's attention by stating they can save Mary $16\%$ per month on her credit card payments. This company charges $15\mathrm{.}5\%$ APR. Is the$$ company's claim$$ correct? Assume a $10-$year repayment period.

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Part $1$

$$Mary$\text{'}$s current minimum monthly payments are