Patrice's credit card has an APR of [tex]$11 \%$[/tex], calculated on the previous monthly balance, and a minimum payment of [tex]$2 \%$[/tex], starting the month after the first purchase. 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]$\$[/tex] 0.00[tex]$ & $[/tex]\[tex]$ 3900.00$[/tex] & [tex]$\$[/tex] 0.00[tex]$ & $[/tex]\[tex]$ 0.00$[/tex] & [tex]$\$[/tex] 0.00[tex]$ & $[/tex]\[tex]$ 3900.00$[/tex] \\
2 & [tex]$\$[/tex] 3900.00[tex]$ & $[/tex]\[tex]$ 0.00$[/tex] & [tex]$\$[/tex] 78.00[tex]$ & $[/tex]\[tex]$ 35.75$[/tex] & [tex]$\$[/tex] 42.25[tex]$ & $[/tex]\[tex]$ 3857.75$[/tex] \\
3 & [tex]$\$[/tex] 3857.75[tex]$ & $[/tex]\[tex]$ 0.00$[/tex] & [tex]$\$[/tex] 77.16[tex]$ & $[/tex]\[tex]$ 35.36$[/tex] & [tex]$\$[/tex] 41.79[tex]$ & $[/tex]\[tex]$ 3815.96$[/tex] \\
4 & [tex]$\$[/tex] 3815.96[tex]$ & $[/tex]\[tex]$ 0.00$[/tex] & [tex]$\$[/tex] 76.32[tex]$ & $[/tex]\[tex]$ 34.98$[/tex] & [tex]$\$[/tex] 41.34[tex]$ & $[/tex]\[tex]$ 3774.62$[/tex] \\
5 & [tex]$\$[/tex] 3774.62[tex]$ & $[/tex]\[tex]$ 0.00$[/tex] & [tex]$\$[/tex] 75.49[tex]$ & $[/tex]\[tex]$ 34.60$[/tex] & [tex]$\$[/tex] 40.89[tex]$ & $[/tex]\[tex]$ 3733.73$[/tex] \\
6 & [tex]$\$[/tex] 3733.73[tex]$ & $[/tex]\[tex]$ 0.00$[/tex] & [tex]$\$[/tex] 74.67[tex]$ & $[/tex]\[tex]$ 34.23$[/tex] & [tex]$\$[/tex] 40.45[tex]$ & $[/tex]\[tex]$ 3693.28$[/tex] \\
7 & [tex]$\$[/tex] 3693.28[tex]$ & $[/tex]\[tex]$ 0.00$[/tex] & [tex]$\$[/tex] 73.87[tex]$ & $[/tex]\[tex]$ 33.86$[/tex] & [tex]$\$[/tex] 40.01[tex]$ & $[/tex]\[tex]$ 3653.27$[/tex] \\
\hline
\end{tabular}

How much of the [tex]$\$[/tex] 3900[tex]$ charge that Patrice made during the first month has been paid off?

A. $[/tex]\[tex]$ 455.51$[/tex]

B. [tex]$\$[/tex] 246.73[tex]$

C. $[/tex]\[tex]$ 40.01$[/tex]

D. [tex]$\$[/tex] 208.77$



Answer :

To determine how much of the \[tex]$3900 charge that Patrice made during the first month has been paid off, we need to look at the principal amounts paid each month over the 7 months period. The principal paid is the amount subtracted from the balance, excluding finance charges. 1. From the table, the principal amounts paid each month are as follows: - Month 2: \$[/tex]42.25
- Month 3: \[tex]$41.79 - Month 4: \$[/tex]41.34
- Month 5: \[tex]$40.89 - Month 6: \$[/tex]40.45
- Month 7: \[tex]$40.01 2. To find the total amount of principal paid over these 7 months, we add these principal amounts together: \[ \text{Total principal paid} = 42.25 + 41.79 + 41.34 + 40.89 + 40.45 + 40.01 \] 3. Adding these amounts: \[ 42.25 + 41.79 + 41.34 + 40.89 + 40.45 + 40.01 = 246.73 \] Thus, the total amount of the \$[/tex]3900 charge that has been paid off is \[tex]$246.73. The correct answer is: B. \$[/tex]246.73