jennifer siegel bought a new ford focus for $18,400. she made a down - payment of $4600 and she financed the…
jennifer siegel bought a new ford focus for $18,400. she made a down - payment of $4600 and she financed the balance at $570.40 a month for 5 years. jennifer decided to pay off her loan at the end of 4 years. find the finance charge, the unearned interest using the rule of 78, and payoff amount. part 1 of 3 the finance charge on the loan was intended to be $20,424, under the original payment plan. part 1 / 3 part 2 of 3 the unearned interest if it is paid off after 4 years is $870.24 (round to the nearest cent.)
Answer
Explanation:
Step1: Calculate the financed amount
The cost of the car is $18400$ and the down - payment is $4600$. So the financed amount $P=18400 - 4600=13800$. The loan is paid at $570.40$ per month for $n = 5\times12=60$ months. The total amount paid back under the original plan is $A = 570.40\times60=34224$. The finance charge $FC=A - P=34224-13800 = 20424$.
Step2: Apply the Rule of 78 for unearned interest
The Rule of 78 sums the digits from 1 to $n$. For $n = 60$, the sum $S=\frac{n(n + 1)}{2}=\frac{60\times(60 + 1)}{2}=1830$. The number of remaining payments after 4 years (48 months) is $m=60 - 48 = 12$. The sum of the digits for the remaining payments $s=\frac{m(m + 1)}{2}=\frac{12\times(12+1)}{2}=78$. The unearned interest $UI$ is calculated as $UI=\text{FC}\times\frac{s}{S}$. Substituting the values, we have $UI = 20424\times\frac{78}{1830}\approx870.24$.
Step3: Calculate the pay - off amount
The pay - off amount is the remaining principal plus the unearned interest. After 48 months of payments, the remaining principal is the amount that would have been paid in the remaining 12 months without interest. The remaining principal $RP=570.40\times12 = 6844.8$. The pay - off amount $POA=RP - UI=6844.8-870.24 = 5974.56$.
Answer:
The unearned interest is $$870.24$ and the pay - off amount is $$5974.56$.