Step 1 :Given the previous balance of \(\$40.33\), purchases of \(\$477.03\) and \(\$220.16\), a payment of \(\$100.00\), and a finance charge of \(\$6.58\).
Step 2 :To find the new balance on October 1, we need to add the previous balance, the purchases, and the finance charge, then subtract the payment.
Step 3 :Using the formula: \(\text{new balance} = \text{previous balance} + \text{purchases1} + \text{purchases2} + \text{finance charge} - \text{payment}\)
Step 4 :Substitute the given values into the formula: \(\text{new balance} = 40.33 + 477.03 + 220.16 + 6.58 - 100.00\)
Step 5 :Calculate the new balance: \(\text{new balance} = 644.10\)
Step 6 :\(\boxed{\text{The new balance on October 1 is }\$644.10}\)