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Math Asked by a SnapAndSolve user · about 2 hours ago

For the three-part question that follows, provide your answer to each part in the given workspace. Identify...

For the three-part question that follows, provide your answer to each part in the given workspace. Identify each part with a coordinating response. Be sure to clearly label each part of your response as Part A, Part B, and Part C.
Christopher borrows $7,500 to build a garage. He agrees to pay $475 a month for 24 months but pays off the loan after 18 months.
Part A: Determine the amount of unearned interest.
Part B: Determine the amount needed to repay the loan using the Rule of 78.
Part C: Show your work to support your answers to Part A and Part B.

Answer

Part A: The amount of unearned interest is calculated using the Rule of 78. The total interest paid over the life of the loan is $475 * 24 - $7,500 = $4,900. The sum of the digits for 24 months is 300 (1+2+...+24). For 18 months, the sum is 171 (1+2+...+18). The unearned interest is (300 - 171) / 300 * $4,900 = $2,107.

Part B: The amount needed to repay the loan using the Rule of 78 is the principal plus the earned interest. The earned interest is 171 / 300 * $4,900 = $2,793. Therefore, the amount needed to repay is $7,500 + $2,793 = $10,293.

Part C:

  1. Calculate total interest: $475 * 24 - $7,500 = $4,900.
  2. Calculate sum of digits for 24 months: 300.
  3. Calculate sum of digits for 18 months: 171.
  4. Calculate unearned interest: (300 - 171) / 300 * $4,900 = $2,107.
  5. Calculate earned interest: 171 / 300 * $4,900 = $2,793.
  6. Calculate total repayment: $7,500 + $2,793 = $10,293.

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