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

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