Joanne Flynn bought a new boat for $16,200. She put a $2,800 down payment on it. The bank’s loan was for 50 months. Finance charges totaled $5,380.00. Assume Joanne decided to pay off the loan at the end of the 22th month. (Rule of 78)
What rebate would she be entitled to and what would be the actual payoff amount? (Do not round intermediate calculations. Round your answers to 2 decimal places. Omit the "$" sign in your response.)
Rebate: $1,845.00
Actual Payoff Amount: $13,535.00
To calculate the rebate Joanne would be entitled to, we need to follow these steps:
1. Determine the total interest charges for the loan.
Loan amount = $16,200 - $2,800 (down payment) = $13,400
Total interest charges = finance charges - interest for the remaining months
2. Calculate the interest for the remaining months.
Total interest = $5,380
Interest per month = Total interest / 50 (months)
Interest for remaining months = Interest per month * (50 - 22) (months)
3. Calculate the rebate.
Rebate = Total interest charges - Interest for remaining months
Now let's calculate:
1. Total interest charges:
Total interest charges = $5,380
2. Calculate the interest for the remaining months:
Interest per month = $5,380 / 50 = $107.60
Interest for remaining months = $107.60 * (50 - 22) = $1,460.80
3. Calculate the rebate:
Rebate = $5,380 - $1,460.80 = $3,919.20
Therefore, Joanne would be entitled to a rebate of $3,919.20.
To calculate the actual payoff amount, we subtract the rebate from the remaining balance:
Remaining balance = Loan amount - (monthly payment * number of remaining months)
Monthly payment = Total loan amount / number of months
Number of remaining months = 50 - 22
Let's calculate:
1. Calculate the monthly payment:
Monthly payment = $13,400 / 50 = $268
2. Calculate the number of remaining months:
Number of remaining months = 50 - 22 = 28
3. Calculate the remaining balance:
Remaining balance = $13,400 - ($268 * 28) = $5,936
The actual payoff amount is $5,936.
To calculate the rebate Joanne would be entitled to and the actual payoff amount, we need to follow these steps:
Step 1: Find the adjusted principal.
The adjusted principal is the original loan amount minus the down payment. In this case, the original loan amount is $16,200 and the down payment is $2,800.
Adjusted principal = $16,200 - $2,800 = $13,400
Step 2: Calculate the unearned finance charges.
The unearned finance charges are calculated using the Rule of 78. The Rule of 78 assigns greater interest weights to the earlier months of the loan. To calculate the unearned finance charges, we need to determine the sum of the digits for the remaining months.
The sum of the digits for 50 months is: 50(51)/2 = 1,275.
Since we're terminating the loan after 22 months, the sum of the digits for the remaining months is: 29(30)/2 = 435.
Now we can calculate the unearned finance charges:
Unearned finance charges = (Remaining months / Total months) * Finance charges
Unearned finance charges = (435 / 1,275) * $5,380.00
Step 3: Calculate the rebate.
The rebate is the difference between the unearned finance charges and the finance charges already paid.
Finance charges already paid = Finance charges - unearned finance charges
Rebate = Finance charges already paid + additional charges
Step 4: Calculate the actual payoff amount.
Actual payoff amount = Adjusted principal + Finance charges already paid - Rebate
Now let's calculate the rebate and the actual payoff amount:
Unearned finance charges = (435 / 1,275) * $5,380.00
Finance charges already paid = $5,380.00 - unearned finance charges
Rebate = Finance charges already paid + additional charges
Actual payoff amount = Adjusted principal + Finance charges already paid - Rebate
Calculating these values will give you the answers.