Use the Rule of 78 to find the payoff amount for the loan paid in full before the date of maturity.
-Finance charge: $23,156 Total number of payments: 281
Amount per payment: $256
Remaining number of payments, when paid in full: 6

Question

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The Rule of 78 is a method used to calculate the interest portion of a loan that is being paid off early. It disproportionately allocates more interest to the early payments of a loan. To find the payoff amount using the Rule of 78, you first calculate the sum of the digits for the total number of payments. For 281 payments, the sum is $1+2+3+...+281$. This sum can be calculated quickly using the formula for the sum of an arithmetic series: $S = \frac{n(n + 1)}{2}$, where $n$ is the total number of payments. So, $S = \frac{281(281 + 1)}{2} = 39561$.Next, calculate the sum of the digits for the remaining number of payments, which is $276+277+278+279+280+281$. This sum is $1671$.The portion of the finance charge to be rebated (not charged) is then calculated by dividing the sum for the remaining payments by the total sum and multiplying by the total finance charge: $\frac{1671}{39561} \times 23156 = 977.73$.The total amount to be paid off is the remaining principal plus the remaining finance charge minus the rebate. However, since we are not given the remaining principal, and the question seems to focus on calculating the finance charge portion that would be rebated or applied, we focus on the finance charge adjustment.Given the finance charge of $23,156 and the calculated rebate of $977.73, the adjusted finance charge is $23,156 - $977.73 = $22,178.27. However, without the remaining principal, we directly address the calculation error and recognize that the correct approach involves calculating the rebate or adjustment to the finance charge due to early payoff. The provided options seem to reflect a misunderstanding of the calculation required or missing information.Given the misunderstanding in the calculation process and the provided options, the correct approach involves recalculating based on the Rule of 78's application to the finance charge and early payoff, but the provided options and information lead to a discrepancy in the expected process. The correct answer should involve calculating the rebate on the finance charge due to early payoff, but without the full loan amount or the principal balance, we cannot accurately determine the payoff amount solely based on the provided information and the typical use of the Rule of 78.

Use the Rule of 78 to Find the Payoff Amount