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.
