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5
8. A machine worth $10,000 new and having a scrap value of $500 is to be depreciated over a ten-year life.
Using the straight-line method for depreciation, answer the following questions. (7 points)
A. What will be the value of the machine after 4 years? (3 points)
B. At what time will the machine be worth $5,000? Round your answer to two decimal places.
Answer: A.____________________ B. Approximately ____________________ years

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**

---

### 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**

---

### Final Answers:
- **Part A:** $6,200
- **Part B:** Approximately 5.26 years

---

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.

A machine worth $10,000 new and having a scrap value of $500 is to be depreciated over a ten-year life. Using the straight-line method for depreciation, answer the following questions. A. What will be the value of the machine after 4 years? B. At what time will the machine be worth $5,000?

Learn how to calculate the value of a machine using the straight-line depreciation method. This problem involves a machine worth $10,000 with a $500 scrap value and a 10-year lifespan. Includes detailed steps to find the machine's value after 4 years and when it will be worth $5,000. Suitable for high school students in Grades 9-12.

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