To determine the finance charge rebate (interest amount credited back) and the final payoff amount for Kelly's car loan, follow these steps:
Step 1: Calculate the total amount paid so far.
The total amount paid so far can be calculated by multiplying the monthly payment by the number of payments made. In this case, Kelly has made 25 monthly payments, so the total amount paid so far is:
Total Amount Paid = Monthly Payment * Number of Payments Made
Total Amount Paid = $382.87 * 25 = $9,571.75
Step 2: Calculate the remaining balance.
The remaining balance can be calculated by subtracting the total amount paid so far from the original loan amount. Since the loan period is 66 months, and she has paid 25 months, there are 66 - 25 = 41 months left.
Remaining Balance = Original Loan Amount - Total Amount Paid So Far
Remaining Balance = (Monthly Payment * Loan Period) - Total Amount Paid So Far
Remaining Balance = ($382.87 * 66) - $9,571.75
Step 3: Calculate the finance charge rebate (interest credited back).
To calculate the finance charge rebate, you need to determine the future value of the remaining balance over the remaining 41 months. This can be done using the future value of an ordinary annuity formula or a financial calculator. However, the interest rate should be converted to a monthly rate by dividing the APR by 12 months.
Monthly Interest Rate = APR / 12 / 100
Monthly Interest Rate = 22.99% / 12 / 100 = 0.01916
Using the future value of an ordinary annuity formula, the finance charge rebate can be calculated as follows:
Finance Charge Rebate = Remaining Balance * (1 - (1 + Monthly Interest Rate)^(-Remaining Months)) / Monthly Interest Rate
Finance Charge Rebate = Remaining Balance * (1 - (1 + 0.01916)^(-41)) / 0.01916
Step 4: Calculate the final payoff amount.
The final payoff amount is the sum of the remaining balance (after the finance charge rebate) and the finance charge rebate itself.
Final Payoff = Remaining Balance - Finance Charge Rebate
By following these steps, you should be able to calculate the finance charge rebate and the final payoff amount for Kelly's car loan.