Sally's credit card has an APR of [tex]31\%[/tex], calculated on the previous monthly balance. Her credit card record for the last 7 months is shown in the table below.

\begin{tabular}{ccccccc}
\hline
\begin{tabular}{c}
End of \\
month
\end{tabular} & \begin{tabular}{c}
Previous \\
balance
\end{tabular} & \begin{tabular}{c}
New \\
charges
\end{tabular} & \begin{tabular}{c}
Payment \\
received
\end{tabular} & \begin{tabular}{c}
Finance \\
charges
\end{tabular} & \begin{tabular}{c}
Principal \\
paid
\end{tabular} & \begin{tabular}{c}
New \\
balance
\end{tabular} \\
\hline
1 & \[tex]$0.00 & \$[/tex]511.00 & \[tex]$0.00 & \$[/tex]0.00 & \[tex]$0.00 & \$[/tex]511.00 \\
2 & \[tex]$511.00 & \$[/tex]62.00 & \[tex]$373.87 & \$[/tex]13.20 & \[tex]$360.67 & \$[/tex]212.33 \\
3 & \[tex]$212.33 & \$[/tex]89.00 & \[tex]$55.89 & \$[/tex]5.49 & \[tex]$50.40 & \$[/tex]250.93 \\
4 & \[tex]$250.93 & \$[/tex]112.00 & \[tex]$177.98 & \$[/tex]6.48 & \[tex]$171.50 & \$[/tex]191.43 \\
5 & \[tex]$191.43 & \$[/tex]49.00 & \[tex]$99.97 & \$[/tex]4.95 & \[tex]$95.02 & \$[/tex]145.40 \\
6 & \[tex]$145.40 & \$[/tex]68.00 & \[tex]$217.16 & \$[/tex]3.76 & \[tex]$213.40 & \$[/tex]0.00 \\
7 & \[tex]$0.00 & \$[/tex]158.00 & \[tex]$28.11 & \$[/tex]0.00 & \$28.11 & ? \\
\hline
\end{tabular}

What is the new balance at the end of month 7?



Answer :

To determine the new balance at the end of month 7, we need to examine the relevant transactions that have taken place within that month. Here is a breakdown of the transactions and how they impact the new balance:

1. Previous Balance:
- At the end of month 6, the balance was \[tex]$0.00. 2. New Charges: - Sally made new charges amounting to \$[/tex]158.00.

3. Payment Received:
- A payment of \[tex]$28.11 was made to the credit card account. 4. Finance Charges: - There are no finance charges for this month (0.00). To calculate the new balance, we follow these steps: \[ \text{New Balance} = \text{Previous Balance} + \text{New Charges} - \text{Payment Received} + \text{Finance Charges} \] Substituting the given values: \[ \text{New Balance} = 0.00 + 158.00 - 28.11 + 0.00 \] Performing the arithmetic: \[ \text{New Balance} = 129.89 \] Therefore, the new balance at the end of month 7 is \$[/tex]129.89.