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2 years ago

8

Suppose that you decide to buy a car for $62000, including taxes and license fees. You saved $ 11000 for a down payment. The d

ealer is offering you a choice between two incentives.
Incentive A is $7000 off the price of the car, followed by a four-year loan at 5.85%.

Incentive B does not have a cash rebate, but provides free financing (no interest) over four years.

The difference in monthly payments between the two offers is what?

1 answer:

ExtremeBDS [4]2 years ago

6 0

Answer:

The difference in monthly payments between the two offers is $32.2

Step-by-step explanation:

He already has $11,000 saved, thus, the amount remaining to pay is $62,000-$11,000 = $51,000

Now, incentive A is taking off 7,000 off the price of the car but the framing amount is a loan at 5.85%

Thus the amount of loan to be taken will be 5.85% on (51,000-7000) = 44,000

So the amount to be paid monthly via incentive A is calculated using the formula below

Monthly payment = P(r/n)/[1-(1+r/n)^-nt]

Where P = 44,000

r is the rate = 5.85% = 5.85/100 = 0.0585

n is the number of months per year = 12

t is the time in years = 4 years

Substituting the values, we have;

Monthly payment = 44,000(0.0585/12)/[1-(1+ 0.0585/12)^-60] = 44,000(0.004875)/[1-(1+0.004875)^-48] = 214.5/(0.2081) = $1030.3

Incentive B however, involves paying the 51,000 over 4 years.

The monthly payment here will be 51,000/48 = $1,062.5

Thus, the difference between the two payments will be;

$1062.5 - $1030.3= $32.2

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