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Suppose Jana borrows $47,100 and agrees to make 60 monthly payments of $995. She decides to pay the debt in...

13. Suppose Jana borrows $47,100 and agrees to make 60 monthly payments of $995. She decides to pay the debt in full after 52 months. Calculate the amount needed to repay her loan in full. Use the Rule of 78.

Answer

Answer: To calculate the amount needed to repay the loan using the Rule of 78, we first need to determine the total interest paid over the life of the loan. The Rule of 78 is a method of allocating the interest charge on a loan across its payment periods. It favors the lender by front-loading interest payments.

1. Calculate the total interest: Total payments = 60 payments × $995 = $59,700. Total interest = $59,700 - $47,100 = $12,600.

2. Calculate the sum of the digits for 60 months: Sum = 60 × (60 + 1) / 2 = 1830.

3. Calculate the sum of the digits for the remaining 8 months: Sum = 8 × (8 + 1) / 2 = 36.

4. Calculate the interest rebate: Interest rebate = ($12,600 × 36) / 1830 = $248.36.

5. Calculate the payoff amount: Payoff amount = Remaining balance + Remaining interest = $47,100 - ($12,600 - $248.36) = $7,712.13.

Therefore, the amount needed to repay the loan in full after 52 months is $7,712.13.

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