To solve this depreciation problem using the straight-line method, we follow these steps:

Given:

• Initial value of the machine (P) = $10,000
• Scrap value (S) = $500
• Lifespan of the machine (N) = 10 years

The straight-line method formula for depreciation is:

$\text{Annual Depreciation (D)} = \frac{P - S}{N}$

In this case:

$D = \frac{10,000 - 500}{10} = \frac{9,500}{10} = 950 \, \text{dollars per year}$

The machine loses $950 in value every year.

Part A: What will be the value of the machine after 4 years?

The value of the machine after 4 years can be calculated by subtracting the depreciation for 4 years from the original value of the machine:

$\text{Value after 4 years} = P - D \times 4$

Substitute the values:

$\text{Value after 4 years} = 10,000 - 950 \times 4$ $\text{Value after 4 years} = 10,000 - 3,800 = 6,200$

Answer for Part A: $6,200

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Part B: At what time will the machine be worth $5,000?

To find the time when the machine will be worth $5,000, we can use the formula for the machine's value after $t$ years:

$\text{Value at year } t = P - D \times t$

We are given the value at year $t$ is $5,000, so:

$5,000 = 10,000 - 950 \times t$

Now, solve for $t$:

$950 \times t = 10,000 - 5,000$ $950 \times t = 5,000$ $t = \frac{5,000}{950} \approx 5.26$

Answer for Part B: Approximately 5.26 years

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Final Answers:

• Part A: $6,200
• Part B: Approximately 5.26 years

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Do you want further details or have any questions?

Here are 5 related questions:

1. How is the depreciation formula derived?
2. What would be the value after 7 years?
3. What is the percentage depreciation per year?
4. What happens if the scrap value changes?
5. How is the straight-line method different from other depreciation methods?

Tip: Straight-line depreciation results in equal expense allocation over the asset's useful life.