Question1 point A $\$ 27,000$ car has a resale value of $\$ 18,000$ five years after it was purchased. Assuming the value of this car depreciates linearly, estimate the value of the car 8 years after it was purchased. Enter your answer rounded to the nearest whole number. Do not enter the $\$$ symbol. Type your answer...
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Studdy Solution

STEP 1

1. The value of the car depreciates linearly over time.
2. The initial value of the car is \$27,000.
3. The value of the car after 5 years is \$18,000.
4. We need to estimate the value of the car 8 years after it was purchased.

STEP 2

1. Determine the rate of linear depreciation per year.
2. Use the depreciation rate to calculate the value of the car after 8 years.

STEP 3

Calculate the total depreciation over the first 5 years. $\text{Total depreciation after 5 years} = \text{Initial value} - \text{Value after 5 years} = 27000 - 18000 = 9000$

STEP 4

Determine the annual depreciation rate by dividing the total depreciation by the number of years. $\text{Annual depreciation rate} = \frac{\text{Total depreciation after 5 years}}{5} = \frac{9000}{5} = 1800$

STEP 5

Calculate the total depreciation over 8 years using the annual depreciation rate. $\text{Total depreciation after 8 years} = \text{Annual depreciation rate} \times 8 = 1800 \times 8 = 14400$

STEP 6

Subtract the total depreciation after 8 years from the initial value to find the estimated value of the car. $\text{Estimated value after 8 years} = \text{Initial value} - \text{Total depreciation after 8 years} = 27000 - 14400 = 12600$
Solution: The estimated value of the car 8 years after it was purchased is \$12,600.

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