Let's solve this step-by-step:
1. Calculate the Product/Sum of Balances and Days:
[tex]\[
\begin{array}{|c|c|c|c|c|c|}
\hline \text{Date} & \text{Payments} & \text{Purchases} & \text{Balance} & \text{Number of Days} & \text{Product/Sum} \\
\hline 9/1-9/5 & & & \$387.52 & 5 & \$1,937.60 \\
\hline 9/6 & \$50.00 & & \$337.52 & 1 & \$337.52 \\
\hline 9/7-9/18 & & & \$387.52 & 11 & \$4,262.72 \\
\hline 9/19 & & \$62.26 & \$399.78 & 1 & \$399.78 \\
\hline 9/20-9/30 & & & 0 & 12 & 0 \\
\hline \text{Total} & & & & 30 & \$6,937.62 \\
\hline
\end{array}
\][/tex]
2. Calculate the Average Daily Balance:
Total sum of product of balances and days = \[tex]$6,937.62
Total number of days = 18
\[
\text{Average daily balance} = \frac{\text{Total sum}}{\text{Total days}} = \frac{6937.62}{18} \approx \$[/tex]385.42
\]
3. Calculate the Finance Charge:
Monthly rate = 1.25% = 0.0125
[tex]\[
\text{Finance charge} = \text{Average daily balance} \times \text{Monthly rate} = 385.42 \times 0.0125 \approx \$4.82
\][/tex]
4. Calculate the New Balance:
Previous balance = \[tex]$387.52
Payment = \$[/tex]50.00
New purchase = \[tex]$62.26
\[
\text{New balance} = \text{Previous balance} - \text{Payment} + \text{Finance charge} + \text{New purchase}
\]
\[
\text{New balance} = 387.52 - 50.00 + 4.82 + 62.26 \approx \$[/tex]404.60
\]
So, summarizing the final results:
- Average daily balance ≈ \[tex]$385.42
- Finance charge ≈ \$[/tex]4.82
- New balance ≈ \$404.60
