Problem

Use the Rule of 78 to determine the unearned interest on a loan with these conditions. \begin{tabular}{|c|c|c|} \hline \begin{tabular}{c} Finance \\ Charge \end{tabular} & \begin{tabular}{c} Total Number \\ of Payments \end{tabular} & \begin{tabular}{c} Remaining Number \\ of Payments when \\ Paid in Full \end{tabular} \\ \hline$\$ 860$ & 48 & 12 \\ \hline \end{tabular} The unearned interest is $\$ \square$. (Round to the nearest cent as needed.)

Solution

Step 1 :The Rule of 78 is a method used by some lenders to calculate the amount of interest a borrower must pay if they pay off their loan early. The rule is named after the sum of the digits 1 through 12 (the number of months in a year), which equals 78.

Step 2 :The formula to calculate the unearned interest using the Rule of 78 is: Unearned Interest = \( \frac{{\text{{Remaining Payments}} \times (\text{{Remaining Payments}} + 1)}}{{\text{{Total Payments}} \times (\text{{Total Payments}} + 1)}} \) * Finance Charge

Step 3 :In this case, the Finance Charge is $860, the Total Number of Payments is 48, and the Remaining Number of Payments when Paid in Full is 12.

Step 4 :Let's plug these values into the formula and calculate the unearned interest.

Step 5 :Unearned Interest = \( \frac{{12 \times (12 + 1)}}{{48 \times (48 + 1)}} \) * 860 = \$57.04

Step 6 :Final Answer: The unearned interest is \(\boxed{\$57.04}\)

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Source: https://solvelyapp.com/problems/V7x5c947aH/

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