A car is purchased for $37,000 and is worth $ 2,600 after 8 years. Assuming the car depreciated in value steadily from year to year, what was it worth at the end of the third year?

Question

$24,100
$24,700
$26,200
None of these

Answer 1

The car's initial value is $37,000 and its value after 8 years is $2,600. To find the annual depreciation, we can perform the following calculations:

1. Calculate the total depreciation over 8 years: \[ \text{Total Depreciation} = \text{Initial Value} - \text{Value after 8 years} \] \[ \text{Total Depreciation} = 37,000 - 2,600 = 34,400 \]

2. Calculate the annual depreciation: \[ \text{Annual Depreciation} = \frac{\text{Total Depreciation}}{8} \] \[ \text{Annual Depreciation} = \frac{34,400}{8} = 4,300 \]

3. Now, to find the car's value at the end of the third year, we will calculate the depreciation for 3 years: \[ \text{Depreciation after 3 years} = 3 \times \text{Annual Depreciation} \] \[ \text{Depreciation after 3 years} = 3 \times 4,300 = 12,900 \]

4. Finally, calculate the value of the car at the end of the third year: \[ \text{Value after 3 years} = \text{Initial Value} - \text{Depreciation after 3 years} \] \[ \text{Value after 3 years} = 37,000 - 12,900 = 24,100 \]

Therefore, the worth of the car at the end of the third year is $24,100.