Question

oy has been saving her earnings to make a down payment on a new car. Which loan terms will result in highest total cost for the loan?


A: 2.5 percent loan for 24 months

B: 3.5 percent loan for 36 months

C: 4.5 percent loan for 48 months

D: 5.5 percent loan for 60 months

Answer 1

@aum

Answer 2

In general, the longer the loan period the higher the total cost. The reason people choose a longer loan is the monthly payment will be lower. But you end up paying a lot more interest in the long run and also you have to pay for many, many months. So based on that we can say the 60 month loan will result in the highest total cost.

Answer 3

But if you are expected to prove it, then you can use the following method:
The formula for monthly payment is:
\[\large M = \frac{Lc(1+c)^n} {(1+c)^n - 1}\]M = Fixed Monthly Payment
L = Total Loan Amount
c = Interest rate in decimal PER MONTH where the interest rate is compounded monthly
n = Total number of monthly payments
For this problem assume L = 1 for all 4 cases.

A. 2.5 percent loan for 24 months
c = 0.025 / 12 = 0.0020833
n = 24 \[\large M = \frac{0.0020833(1.0020833)^{24}} {(1.0020833)^{24} - 1} = ?\]Then multiply monthly payment M by total number of payments n (n is 24 here) to get the total amount paid.

Use the same procedure to calculate the total amount paid for each of the other answer choices. See which one results in the highest total cost for the loan.