Suppose you take out a loan for 180 days in the amount of $13,500 at 11% ordinary interest. After 50 days, you make a partial payment of $1,000. What is the final amount due on the loan? (Round to the nearest cent)
A) $13,210.97
B) $13,698.82
C) $13,242.50
D) $13,232.33

Question

Quizplus · Accepted Answer

First, calculate the interest on the original loan for 180 days: Interest = Principal × Rate × Time = $13,500 × 11% × (180/360) = $742.50. After 50 days, a payment of $1,000 is made, reducing the principal to $12,500. The interest on the new principal for the remaining 130 days is: Interest = $12,500 × 11% × (130/360) = $401.04. The total amount due is the new principal plus the total interest: $12,500 + $742.50 + $401.04 = $13,643.54. However, since the payment reduces the principal before the total interest calculation, the correct approach is to first calculate the interest for 50 days on the original amount, then reduce the principal and calculate the remaining interest. Correcting this: Initial interest for 50 days = $13,500 × 11% × (50/360) = $206.25. New principal after payment = $13,500 - $1,000 = $12,500. Remaining interest for 130 days = $12,500 × 11% × (130/360) = $401.04. Total interest = $206.25 + $401.04 = $607.29. Final amount due = $12,500 + $607.29 = $13,107.29. The calculation provided does not match any of the options exactly due to a mistake in the interest calculation steps. The correct method involves calculating the interest before and after the payment, then summing those interests with the reduced principal. The error in calculation led to an incorrect conclusion. The correct calculation should consider the impact of the partial payment on both the reduction of principal and the adjustment of interest accrued before and after the payment. The final amount due involves calculating the interest up to the payment, reducing the principal by the payment amount, then calculating the interest on the new principal for the remainder of the term. The correct answer, based on the initial calculation method provided, was not accurately derived due to a miscalculation of the interest and the effect of the partial payment. To accurately determine the final amount due, one must correctly apply the formula for ordinary interest, adjust the principal after the partial payment, and calculate the interest on the adjusted principal for the remaining term.

Suppose You Take Out a Loan for 180 Days in the Amount