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Sonja's credit card has an APR of [tex]$21 \%$[/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}{l}
Payment \\
received
\end{tabular} & \begin{tabular}{l}
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]$ 700.00$[/tex] & [tex]$\$[/tex] 0.00[tex]$ & $[/tex]\[tex]$ 0.00$[/tex] & [tex]$\$[/tex] 0.00[tex]$ & $[/tex]\[tex]$ 700.00$[/tex] \\
2 & [tex]$\$[/tex] 700.00[tex]$ & $[/tex]\[tex]$ 0.00$[/tex] & [tex]$\$[/tex] 14.00[tex]$ & $[/tex]\[tex]$ 12.25$[/tex] & [tex]$\$[/tex] 1.75[tex]$ & $[/tex]\[tex]$ 698.25$[/tex] \\
3 & [tex]$\$[/tex] 698.25[tex]$ & $[/tex]\[tex]$ 0.00$[/tex] & [tex]$\$[/tex] 13.97[tex]$ & $[/tex]\[tex]$ 12.22$[/tex] & [tex]$\$[/tex] 1.75[tex]$ & $[/tex]\[tex]$ 696.50$[/tex] \\
4 & [tex]$\$[/tex] 696.50[tex]$ & $[/tex]\[tex]$ 0.00$[/tex] & [tex]$\$[/tex] 13.93[tex]$ & $[/tex]\[tex]$ 12.19$[/tex] & [tex]$\$[/tex] 1.74[tex]$ & $[/tex]\[tex]$ 694.76$[/tex] \\
5 & [tex]$\$[/tex] 694.76[tex]$ & $[/tex]\[tex]$ 0.00$[/tex] & [tex]$\$[/tex] 13.90[tex]$ & $[/tex]\[tex]$ 12.16$[/tex] & [tex]$\$[/tex] 1.74[tex]$ & $[/tex]\[tex]$ 693.03$[/tex] \\
6 & [tex]$\$[/tex] 693.03[tex]$ & $[/tex]\[tex]$ 0.00$[/tex] & [tex]$\$[/tex] 13.86[tex]$ & $[/tex]\[tex]$ 12.13$[/tex] & [tex]$\$[/tex] 1.73[tex]$ & $[/tex]\[tex]$ 691.29$[/tex] \\
7 & [tex]$\$[/tex] 691.29[tex]$ & $[/tex]\[tex]$ 0.00$[/tex] & [tex]$\$[/tex] 13.83[tex]$ & $[/tex]\[tex]$ 12.10$[/tex] & [tex]$\$[/tex] 1.73[tex]$ & $[/tex]\[tex]$ 689.57$[/tex] \\
\hline
\end{tabular}

About what percentage of Sonja's payments so far have gone to paying interest?



Answer :

GinnyAnswer
To determine what percentage of Sonja’s payments so far have gone to paying interest, let's break the problem down step by step:

1. Identify Total Interest Paid:
We need to sum up the finance charges (interest) over the 7 months.

[tex]\[ \text{Total interest paid} = 0 + 12.25 + 12.22 + 12.19 + 12.16 + 12.13 + 12.10 = 73.05 \][/tex]

2. Identify Total Payments Made:
We need to sum up all the payments received over the 7-month period.

[tex]\[ \text{Total payments received} = 0 + 14 + 13.97 + 13.93 + 13.90 + 13.86 + 13.83 = 83.49 \][/tex]

3. Calculate the Percentage of Payments that Went to Interest:
To find the percentage of the total payments that were used to pay interest, use the formula:

[tex]\[ \text{Percentage interest} = \left( \frac{\text{Total interest paid}}{\text{Total payments received}} \right) \times 100 \][/tex]

Substituting the values we computed:

[tex]\[ \text{Percentage interest} = \left( \frac{73.05}{83.49} \right) \times 100 \approx 87.50 \% \][/tex]

Thus, approximately [tex]\(87.50\%\)[/tex] of Sonja's payments so far have gone to paying interest.

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