determine finance charge rebate. Kelly has a 66 month car loan monthly payments of 382.87. the APR is 22.99%. so far Kelly has paid 25 monthly payments, next week she will receive an inheritance and wants to pay off the loan, there are 41 months left what should the interest amount be credited back to the account and what should the final pay off be?
Good heavens!
You didn't just multiply 283.87 by 66, but you must have!!
That would be totally invalid and violates all rules of actuarial mathematics.
You have totally ignored the rather hefty interest rate of 22.9% !!!!
Trust me, the method I used is mathematically correct
The balance remaining after 25 payments is $13954.48 , which is what my calculation ends up as.
I even made up a spreadsheet with headings of
payment # , payment, interest, repayment, balance
0 0 0 0 14301.27
1 283.87 272.915902 10.95409798 14290.3159
2 283.87 272.7068613 11.16313868 14279.15276
3 283.87 272.4938314 11.37616858 14267.77659
4 283.87 272.2767362 11.59326379 14256.18333
5 283.87 272.0554981 11.81450191 14244.36883
6 283.87 271.830038 12.03996199 14232.32887
7 283.87 271.6002754 12.26972459 14220.05914
8 283.87 271.3661282 12.50387184 14207.55527
9 283.87 271.1275126 12.74248739 14194.81278
10 283.87 270.8843435 12.98565653 14181.82713
11 283.87 270.6365339 13.23346614 14168.59366
12 283.87 270.3839952 13.48600478 14155.10766
13 283.87 270.1266373 13.74336271 14141.36429
14 283.87 269.8643681 14.00563188 14127.35866
15 283.87 269.597094 14.27290602 14113.08576
16 283.87 269.3247194 14.54528064 14098.54047
17 283.87 269.0471469 14.82285308 14083.71762
18 283.87 268.7642775 15.10572253 14068.6119
19 283.87 268.4760099 15.39399006 14053.21791
20 283.87 268.1822413 15.68775871 14037.53015
21 283.87 267.8828666 15.98713344 14021.54302
22 283.87 267.5777788 16.29222123 14005.2508
23 283.87 267.2668689 16.60313112 13988.64766
24 283.87 266.9500258 16.9199742 13971.72769
25 283.87 266.6271363 17.24286371 13954.48483
Too bad the columns don't line up nicely, that is the fault of this webpage.
Notice my last entry is the same as my single line calculation from above
I would find what the present value of the loan was:
i = .229/12 = .01908333...
payment = 382.87
n = 66
PV = 382.87(1 - 1.01908333..^-66)/.01908333.. = 14301.27
amount owing after 25 payments = 14301.27(1.01908333..)25 - 382.87(1 + 1.01908333..^25)/.01908333.. = ... (what is owing after making the 25th payment)
That's basically all you need, since that is what is outstanding on the loan.
I don't know how the "next week" part enters the picture, nor
do I understand what you mean by "what should the interest amount be credited back to the account"
Under the contract of the 66 months the total finance charge is $10996.18, total of payments for the 66 month contract term would have been $25,269.42. I have made 25 timely payments of $382.87 which totals $9571.75 If I pay the car of 41 months "early" for interest that has already been pre-computed for the entire term, I'm obviously not going to send them a check for $15,697.67 for the remaining 41 months that the contract will not be open, they have no right to interest that is essentially unearned. I was just hoping someone could help me with the estimated amount that I may owe based on the information I provided.
Thank you for explaining it and breaking it down. You are awesome!!
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.