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.