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 this $" sign in your response.). Ok I add 16,200 to 2,800 and I got 19,000. Then I add 19,000 to 5,380 which is equal to 24,380, 50-22=28. Then I use the rule of 78 to get the rebate. 22=406, 50=1,275. 406/1,275*5,380= 1,713.16. Then I divide 24,380/50=487.60. Then I started to find the final payment 487.60*28=13,652.80-1,713.16=11,939.64 which is the final payment. When I click check my work, it shows that 11,939.64 was not the payment. I got the right rebate, but I need the right answer for the final payment. I need to know what am I doing wrong ? Can someone help me.
To calculate the rebate and the actual payoff amount correctly, we need to use the Rule of 78 method. Here's how you can solve it step by step:
1. Calculate the total amount financed:
The total cost of the boat is $16,200, and Joanne made a down payment of $2,800. Therefore, the amount financed is $16,200 - $2,800 = $13,400.
2. Calculate the finance charges per month:
The finance charges totaled $5,380 over 50 months. Divide the finance charges by the number of months to get the monthly finance charges:
$5,380 / 50 = $107.60 per month.
3. Calculate the rebate:
The Rule of 78 calculates the rebate proportional to the remaining months' interest charges. Since Joanne decided to pay off the loan at the end of the 22nd month, there are remaining (50 - 22) = 28 months.
To calculate the numerator of the rebate formula, multiply the remaining months by the original month number for the sum-of-digits:
Remaining numerator = 28 * (50 + 1) = 28 * 51 = 1,428.
To calculate the denominator of the rebate formula, calculate the sum of the first 50 digits (1 to 50) using the sum formula: (n * (n + 1)) / 2, where n is the number of months.
Total denominator = (50 * (50 + 1)) / 2 = 25 * 51 = 1,275.
Now, calculate the rebate:
Rebate = (Remaining numerator / Total denominator) * Finance charges
= (1,428 / 1,275) * 5,380
= 6.552941176 * 5,380
= $8,653.53 (rounded to 2 decimal places).
4. Calculate the actual payoff amount:
To find the payoff amount, add the remaining finance charges to the amount financed and subtract the rebate:
Payoff amount = Amount financed + Finance charges - Rebate
= $13,400 + (107.60 * 28) - $8,653.53
= $13,400 + $3,010.40 - $8,653.53
= $7,756.87 (rounded to 2 decimal places).
Therefore, the rebate that Joanne would be entitled to is $8,653.53, and the actual payoff amount would be $7,756.87.