A car was purchased for $10,000 with a salvage value of $4000. It is expected to have a useful life of 5 years. Using the sum-of-years method, find the car's value in the first year after the purchase.

To find the car's value in the first year using the sum-of-years method, you need to follow these steps:

1. Calculate the total depreciable cost of the car by subtracting the salvage value from the initial purchase price:
Depreciable cost = Initial purchase price - Salvage value
Depreciable cost = $10,000 - $4,000
Depreciable cost = $6,000

2. Calculate the sum of the years of the useful life of the car:
Sum of the years = 1 + 2 + 3 + 4 + 5
Sum of the years = 15

3. Determine the depreciation expense for the first year by dividing the depreciable cost by the sum of the years and multiplying the result by the remaining useful life:
Depreciation expense = (Depreciable cost / Sum of the years) * Remaining useful life
Depreciation expense = ($6,000 / 15) * 5
Depreciation expense = $2,000

4. Finally, calculate the car's value in the first year by subtracting the depreciation expense from the initial purchase price:
Car's value in the first year = Initial purchase price - Depreciation expense
Car's value in the first year = $10,000 - $2,000
Car's value in the first year = $8,000

Therefore, the car's value in the first year after the purchase, using the sum-of-years method, is $8,000.

To find the car's value in the first year after the purchase using the sum-of-years method, follow these steps:

Step 1: Calculate the total number of years the car is expected to be in use, which is 5 years.

Step 2: Calculate the sum of the years by using the formula (n * (n + 1)) / 2, where n is the total number of years. In this case, it is (5 * (5 + 1)) / 2, which equals 15.

Step 3: Determine the weight for the first year. To calculate this, use the formula (n - x + 1) / sum of the years, where n is the total number of years and x is the specific year. In this case, x represents the first year, so it will be (5 - 1 + 1) / 15, which equals 1/3.

Step 4: Calculate the depreciation for the first year by subtracting the salvage value from the purchase value, which is $10,000 - $4,000 = $6,000.

Step 5: Multiply the depreciation in step 4 by the weight in step 3 to find the car's value in the first year. In this case, it will be $6,000 * 1/3 = $2,000.

Therefore, the car's value in the first year after the purchase using the sum-of-years method is $2,000.

The car is expected to decrease in value $6,ooo in five years (10,000 - 4,000). How much is that per year? Then subtract the yearly depreciation from the purchase price to find the value at the end of the first year.