Richard brought a new car for $39905. He made a down payment of $15000 and payments are $614 monthly for 4 years. At the end of 30 months he was able to payoff the loan using the Rule 78
a. Find he unearned interest
b. Find the payoff
To find the unearned interest and the payoff, we need to understand the Rule of 78. The Rule of 78 is a method used to calculate the interest given the loan's term and payment schedule. It assumes that the interest is paid in proportion to the remaining principal balance over the life of the loan.
First, let's calculate the total interest paid over the 4-year loan term using the monthly payment of $614.
Total interest paid = (monthly payment x loan term) - loan amount
Total interest paid = ($614 x 48) - $39,905
Total interest paid = $29,472 - $39,905
Total interest paid = -$10,433
Please note that the negative value indicates that the interest collected is less than the total payments made. This is because the loan was paid off early, reducing the amount of interest collected.
a. To find the unearned interest at the end of 30 months, we need to calculate the interest that would have been collected if the loan had been paid off completely. We can use the Rule of 78 for this calculation.
Total interest for the loan = (loan term x (loan term + 1))/2 x (total interest paid)
Total interest for the loan = (48 x (48 + 1))/2 x (-$10,433)
Total interest for the loan = (48 x 49)/2 x (-$10,433)
Total interest for the loan = 24 x 49 x (-$10,433)
Total interest for the loan = -$12,149,632
Unearned interest = Total interest for the loan - Total interest paid
Unearned interest = -$12,149,632 - (-$10,433)
Unearned interest = -$12,149,632 + $10,433
Unearned interest = -$12,139,199
The unearned interest at the end of 30 months is -$12,139,199.
b. Now, let's find the payoff amount at the end of 30 months. The payoff amount is the remaining principal balance at that time.
Principal balance remaining = loan amount - (monthly payment x number of months already paid)
Principal balance remaining = $39,905 - ($614 x 30)
Principal balance remaining = $39,905 - $18,420
Principal balance remaining = $21,485
The payoff amount at the end of 30 months is $21,485.