To determine the percentage of Sonja's payments that have gone towards paying the interest on her credit card, we need to follow these steps:
1. Sum of Total Payments:
Sum all the monthly payments Sonja has made over the 7-month period.
2. Sum of Total Finance Charges:
Sum all the monthly finance charges that have been added to her account.
3. Calculate the Percentage of Payments Gone to Interest:
To find the percentage, divide the total finance charges by the total payments made and multiply by 100.
Let's break this down:
1. Calculate the Total Payments:
Adding up each month's payment received:
[tex]\[
\$14.00 + \$13.97 + \$13.93 + \$13.90 + \$13.06 + \$13.83 = \$82.69
\][/tex]
2. Calculate the Total Finance Charges:
Adding up each month's finance charges:
[tex]\[
\$12.25 + \$12.22 + \$12.19 + \$12.16 + \$12.13 + \$12.10 = \$73.05
\][/tex]
3. Calculate the Percentage of Payments that Went to Interest:
Using the totals, we calculate the percentage:
[tex]\[
\text{Percentage} = \left(\frac{\$73.05}{\$82.69}\right) \times 100 \approx 88.34\%
\][/tex]
So, approximately 88.34% of Sonja's payments have gone towards paying the interest.
Considering the options provided, the answer closest to 88.34% is:
A. [tex]\(87\%\)[/tex]
Hence, the correct answer is:
A. 87%
This detailed step-by-step solution shows how we determine the percentage of payments that went towards interest and helps in understanding that option A. 87% is the closest correct answer.
