Josephine purchase a computer for $4,590. the computer decrease in value at a constant rate for 9 years, after which it is considered not to have any monetary value. How much is the computer worth 6 years after it is purchased?

Options

A. 1530
B. 2295
C. 3060
D. 4080

Answer

To find out how much Josephine's computer is worth 6 years after it was purchased, we can follow these steps:

### Step 1: Determine the initial value of the computer
The initial value of the computer is given as:
\[ \text{Initial Value} = 4590 \text{ dollars} \]

### Step 2: Determine the final value of the computer after 9 years
According to the problem, the computer is considered to have no monetary value after 9 years. Therefore:
\[ \text{Final Value after 9 years} = 0 \text{ dollars} \]

### Step 3: Calculate the total depreciation over 9 years
The total depreciation (the amount the computer loses in value) is the difference between the initial value and the final value:
\[ \text{Total Depreciation} = \text{Initial Value} - \text{Final Value} = 4590 - 0 = 4590 \text{ dollars} \]

### Step 4: Calculate the annual depreciation rate
Since the depreciation occurs at a constant rate over 9 years, we can find the annual depreciation rate by dividing the total depreciation by the number of years:
\[ \text{Annual Depreciation Rate} = \frac{\text{Total Depreciation}}{\text{Number of Years}} = \frac{4590}{9} = 510 \text{ dollars per year} \]

### Step 5: Calculate the total depreciation after 6 years
To find out how much value the computer has lost after 6 years, we multiply the annual depreciation rate by the number of years:
\[ \text{Depreciation after 6 years} = \text{Annual Depreciation Rate} \times 6 = 510 \times 6 = 3060 \text{ dollars} \]

### Step 6: Calculate the worth of the computer after 6 years
Now, we can find the worth of the computer after 6 years by subtracting the depreciation after 6 years from the initial value:
\[ \text{Worth after 6 years} = \text{Initial Value} - \text{Depreciation after 6 years} = 4590 - 3060 = 1530 \text{ dollars} \]

### Final Answer
Thus, the worth of the computer 6 years after it is purchased is:
\[ \text{Worth of the computer} = 1530 \text{ dollars} \]

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