Final answer:
The interest paid in the 13th installment is most likely $84.57 because as the remaining balance of the loan decreases, less interest accrues over time. Estimating the rate of decrease from previous payments helps in determining the answer.
Step-by-step explanation:
The interest in a loan paid with equal installments diminishes with each payment since the remaining principal decreases. This is because each installment covers both interest and part of the principal, so as the principal gets smaller, so does the interest portion of each payment. In this problem, we notice a pattern in the decrease of interest between payments in the 4th and 10th years: $168 - $117 = $51 over 6 years. To find the interest paid in the 13th installment, we can assume approximately the same rate of decrease continues.
If the interest decreases by approximately $51 over 6 years, then over 3 years (from the 10th to the 13th year), it would decrease by about half of that amount: $51 / 2 = $25.50. Thus, the estimated interest paid in the 13th installment is $117 - $25.50 = $91.50. However, note that the actual decrease tends to be slightly less each period due to the reducing principal and since the decrease from the 4th to the 10th year may not represent a linear trend, the actual interest for the 13th installment is more likely to be slightly higher. Therefore, the closest answer choice to our calculated value is $84.57, making option C the most probable answer.