Question

Two cars with the same purchase price are not worth the same amount at the end of the year. Some cars depreciate faster than others. A truck depreciates at 45%45% and a Jeep depreciates at 25%25% per year. Assume the initial purchase price is $19,000$19,000 and the total cost of ownership is $38,000$38,000. Use a spreadsheet to determine how much more the Jeep is worth in three years.

a)$11000
b)$3800
c)$11400
d)$10,400

Answer 1

The correct answer is option c) $11,400. Using a depreciation formula, we calculate the value of both a truck and a Jeep after three years of depreciation at different rates (45% for the truck and 25% for the Jeep) from an initial price of $19,000 to determine how much more the Jeep is worth.

Step-by-step explanation:

The correct answer is option c) $11,400. To determine how much more the Jeep is worth after three years, we calculate the value of both vehicles after depreciation. For the truck, with a 45% depreciation per year, the value after one year is 55% of the initial price. Using the initial price of $19,000, after one year, the truck is worth 0.55 x $19,000 = $10,450. Continuing this calculation for three years using the formula V = P(1 - r)^t, where V is the final value, P is the initial price, r is the depreciation rate, and t is time in years, the truck's value would be $19,000 x (1 - 0.45)^3.

Similarly, for the Jeep with 25% depreciation, after one year, it's worth 75% of its initial price, or 0.75 x $19,000. Again, we apply the formula V = P(1 - r)^t for three years, the Jeep's value would be $19,000 x (1 - 0.25)^3.

Once we calculate both values, we can subtract the remaining value of the truck from the remaining value of the Jeep to find out how much more the Jeep is worth after three years.

To determine how much more the Jeep is worth in three years, we need to calculate the depreciation of both vehicles. Given that the truck depreciates at a rate of 45% per year and the Jeep depreciates at a rate of 25% per year, we can use the formula:

Jeep Worth = Purchase Price - (Depreciation Rate * Purchase Price * Number of Years)

Truck Worth = Purchase Price - (Depreciation Rate * Purchase Price * Number of Years)

Plugging in the values, we get:

Jeep Worth = $19,000 - (0.25 * $19,000 * 3) = $19,000 - $14,250 = $4,750

Truck Worth = $19,000 - (0.45 * $19,000 * 3) = $19,000 - $25,650 = -$6,650

Since the truck has a negative worth, we can assume it is not worth anything at the end of three years. Therefore, the Jeep is worth $4,750 more than the truck.