Let's continue to fill in the table and explain the calculations for each step.
We know that each monthly payment is [tex]\(\$ 175.83\)[/tex] and the interest rate is 10% annually, which translates to [tex]\(\frac{10\%}{12} = 0.8333\%\)[/tex] per month.
We'll start from the 7th payment, as the previous entries are already filled.
### Payment 7:
- Monthly Payment: \[tex]$175.83
- New Principal before Payment 7: \$[/tex]857.60
- Interest:
- [tex]\(\$857.60 \times 0.008333 \approx \$8.54\)[/tex]
- Amount for Principal:
- [tex]\(\$175.83 - \$8.54 \approx \$167.29\)[/tex]
- New Principal after Payment 7:
- [tex]\(\$857.60 - \$167.29 \approx \$690.31\)[/tex]
### Payment 8:
- Monthly Payment: \[tex]$175.83
- New Principal before Payment 8: \$[/tex]690.31
- Interest:
- [tex]\(\$690.31 \times 0.008333 \approx \$5.75\)[/tex]
- Amount for Principal:
- [tex]\(\$175.83 - \$5.75 \approx \$170.08\)[/tex]
- New Principal after Payment 8:
- [tex]\(\$690.31 - \$170.08 \approx \$521.63\)[/tex]
Thus, after filling in our table with this information, the entries will look like this:
\begin{center}
\begin{tabular}{|c|c|c|c|c|}
\hline
\begin{tabular}{l}
Payment \\
Number
\end{tabular}
& \begin{tabular}{l}
Monthly \\
Payment
\end{tabular}
& \begin{tabular}{l}
Amount For \\
Interest
\end{tabular}
& \begin{tabular}{l}
Amount for \\
Principal
\end{tabular}
& \begin{tabular}{l}
New Principal
\end{tabular}
\\
\hline
1 & \[tex]$175.83 & \$[/tex]16.67 & \[tex]$159.19 & \$[/tex]1840.81 \\
\hline
2 & \[tex]$175.83 & \$[/tex]15.34 & \[tex]$160.49 & \$[/tex]1680.32 \\
\hline
3 & \[tex]$175.83 & \$[/tex]14.00 & \[tex]$161.83 & \$[/tex]1518.49 \\
\hline
4 & \[tex]$175.83 & \$[/tex]12.65 & \[tex]$163.18 & \$[/tex]1355.31 \\
\hline
5 & \[tex]$175.83 & \$[/tex]11.29 & \[tex]$164.54 & \$[/tex]1190.77 \\
\hline
6 & \[tex]$175.83 & \$[/tex]9.92 & \[tex]$165.91 & \$[/tex]857.60 \\
\hline
7 & \[tex]$175.83 & \$[/tex]8.54 & \[tex]$167.29 & \$[/tex]690.31 \\
\hline
8 & \[tex]$175.83 & \$[/tex]5.75 & \[tex]$170.08 & \$[/tex]521.63 \\
\hline
\end{tabular}
\end{center}
The new principal after the 8th payment is \$521.63.
