To determine the percentage of Sonja's payments that have gone towards paying interest, we need to follow these steps systematically:
1. Identify the Total Finance Charges:
According to the table, the finance charges over the 7 months are as follows:
- Month 1: [tex]$0.00
- Month 2: $[/tex]12.25
- Month 3: [tex]$12.22
- Month 4: $[/tex]12.19
- Month 5: [tex]$12.16
- Month 6: $[/tex]12.13
- Month 7: [tex]$12.10
Summing up these charges:
\[
0.00 + 12.25 + 12.22 + 12.19 + 12.16 + 12.13 + 12.10 = 73.05
\]
So, the total finance charges are \$[/tex]73.05.
2. Identify the Total Payments Received:
According to the table, the payments Sonja made are:
- Month 1: [tex]$0.00
- Month 2: $[/tex]14.00
- Month 3: [tex]$13.97
- Month 4: $[/tex]13.93
- Month 5: [tex]$13.90
- Month 6: $[/tex]13.86
- Month 7: [tex]$13.83
Summing up these payments:
\[
0.00 + 14.00 + 13.97 + 13.93 + 13.90 + 13.86 + 13.83 = 83.49
\]
So, the total payments received are \$[/tex]83.49.
3. Calculate the Percentage of Payments that Went to Paying Interest:
To find this percentage, we use the formula:
[tex]\[
\text{Interest Percentage} = \left( \frac{\text{Total Finance Charges}}{\text{Total Payments Received}} \right) \times 100
\][/tex]
Substituting the values, we get:
[tex]\[
\left( \frac{73.05}{83.49} \right) \times 100 \approx 87.50\%
\][/tex]
Thus, approximately 87.50% of Sonja's payments have gone towards paying interest. The closest answer choice is:
D. [tex]$87\%$[/tex]
