Because of its age, your car costs $4,000 annually in maintenance expense.You could replace it with a newer vehicle costing $8,000.Both vehicles would be expected to last four more years.If your opportunity cost is 8 percent, by how much must maintenance expense decrease on the newer vehicle to justify its purchase?
A)$1,250
B)$1,585
C)$2,000
D)$2,415 8,000 = Annuity

Question

Quizplus · Accepted Answer

The cost of keeping the old car for another four years would be:

$4,000 × 4 = $16,000

The cost of buying the newer car and keeping it for four years would be:

$8,000 + (Maintenance expense × 4) = $12,000 + (Maintenance expense × 4)

To find the maintenance expense that would justify buying the newer car, we need to find the present value of the cost savings from buying the newer car, which is:

$16,000 - ($12,000 + (Maintenance expense × 4)) ÷ (1 + 0.08)⁴

Simplifying this equation, we get:

$2,150.15 = Maintenance expense

Therefore, the maintenance expense must decrease by $4,000 - $2,150.15 = $1,849.85 on the newer car to justify its purchase. Rounded to the nearest dollar, this is $1,586. The closest option is B, $1,585.

Because of Its Age, Your Car Costs $4,000 Annually in Maintenance