She makes the purchase for $552.86.
After one month, she owes $552.86 + the interest of that month.
One month's interest is 27.3%/12 on the balance, so $552.86 * 0.273/12 = $12.58
At the end of the first month, she owes $552.86 + $12.58 = $565.44.
She pays $195. Now she owes $565.44 - $195 = $370.44
After the second month, she owes $370.44 + interst of that month.
One month's interest is 27.3%/12 on the balance, so $370.44 * 0.273/12 = $8.43
At the end of the second month, she owes $370.44 + $8.43 = $378.87
She pays $195. Now she owes $378.87 - $195 = $183.87
After the third month, she owes $183.87 + interest of that month.
One month's interest is 27.3%/12, so $183.87 * 0.273/12 = $4.18
At the end of the third month, she owes $183.87 + $4.18 = $188.05
She pays $188.05 and pays it off.
The total amount she paid was $195 + $195 + $188.05 = $578.05
