12.value:
10.00 points Joanne Flynn bought a new boat for $15,400. She put a $2,600 down payment on it. The bank’s loan was for 46 months. Finance charges totaled $4,859.86. Assume Joanne decided to pay off the loan at the end of the 24th month. (Rule of 78)
What rebate would she be entitled to and what would be the actual payoff amount? (Do not round intermediate calculations. Round your answers to 2 decimal places. Omit the "$" sign in your response.)
Rebate $
Payoff amount
To calculate the rebate and payoff amount using the Rule of 78, we need to follow these steps:
Step 1: Calculate the sum of the digits (SOD) for the loan term.
The loan term is 46 months, so we sum the digits 1 to 46:
SOD = (46 * (46 + 1)) / 2 = 46 * 47 / 2 = 1081
Step 2: Calculate the unearned finance charges for the remaining months.
Since Joanne decided to pay off the loan at the end of the 24th month, there are 46 - 24 = 22 remaining months.
Unearned finance charges = (Finance charges / SOD) * (SOD - Sum of digits from 1 to 24)
Unearned finance charges = (4859.86 / 1081) * ((46 * (46 + 1)) / 2 - (24 * (24 + 1)) / 2)
Unearned finance charges ≈ 4859.86 / 1081 * (1056 - 300) ≈ 4859.86 / 1081 * 756 ≈ 3392.97
Step 3: Calculate the rebate.
Rebate = Finance charges - Unearned finance charges
Rebate = 4859.86 - 3392.97 ≈ 1466.89
Step 4: Calculate the payoff amount.
Payoff amount = Loan amount - Down payment - Rebate
Payoff amount = 15400 - 2600 - 1466.89 ≈ 11333.11
Therefore, according to the Rule of 78, Joanne would be entitled to a rebate of approximately $1466.89, and the actual payoff amount would be approximately $11333.11.