Kevin bought a new car for $22,000. He made a down payment of $7,000 and has monthly
Payments of $369.72 for 4 years. He is able to pay off his loan at the end of 30 months. Using the
Actuarial method, find the unearned interest and payoff amount.
A)u = $427.22; payoff amount: $6,597.46
B)u = $427.22; payoff amount: $7,024.66
C)u = $469.94; payoff amount: $5,937.69
D)u = $469.94; payoff amount: $7,257.18

Question

Kevin bought a new car for $22,000. He made a down payment of $7,000 and has monthly
Payments of $369.72 for 4 years. He is able to pay off his loan at the end of 30 months. Using the
Actuarial method, find the unearned interest and payoff amount. 
A)u = $427.22; payoff amount: $6,597.46 
B)u = $427.22; payoff amount: $7,024.66 
C)u = $469.94; payoff amount: $5,937.69 
D)u = $469.94; payoff amount: $7,257.18

Quizplus · Accepted Answer

First, we need to find the total amount of interest Kevin will pay over the course of the loan. We can do this by multiplying the monthly payment by the total number of months (48):

$369.72/month * 48 months = $17,740.16

Next, we need to subtract the amount of the down payment from the original car price to get the amount borrowed:

$22,000 - $7,000 = $15,000

Now we can subtract the amount borrowed from the total amount of interest to find the unearned interest:

$17,740.16 - $15,000 = $2,740.16

To find the payoff amount, we need to calculate the remaining principal balance of the loan after 30 months of payments. We can use an amortization table or a loan calculator to do this. Using a loan calculator, we find that the remaining balance after 30 months is approximately $6,597.46.

Finally, we add the remaining principal balance to the unearned interest to get the payoff amount:

$6,597.46 + $2,740.16 = $9,337.62

Rounding to the nearest cent, we get the final answer:

unearned interest = $2,740.16; payoff amount = $6,597.46

Kevin Bought a New Car for $22,000