The value of an equipment depreciates by 20% each year. How much less will the value of the equipment be after 3 years?

Options

A. 0.488
B. 0.512
C. 0.54
D. 0.6

Answer

To find out how much less the value of the equipment will be after 3 years due to a 20% annual depreciation, we can follow these steps:

### Step 1: Understand the Depreciation Rate
The equipment depreciates by 20% each year. This means that at the end of each year, the value of the equipment will be 80% of its value at the beginning of that year.

### Step 2: Calculate the Value After Each Year
Let’s assume the initial value of the equipment is \( V \).

1. **After Year 1:**
\[ \text{Value after Year 1} = V \times (1 - 0.20) = V \times 0.80 \]

2. **After Year 2:**
\[ \text{Value after Year 2} = \text{Value after Year 1} \times 0.80 = V \times 0.80 \times 0.80 = V \times 0.80^2 \]

3. **After Year 3:**
\[ \text{Value after Year 3} = \text{Value after Year 2} \times 0.80 = V \times 0.80^2 \times 0.80 = V \times 0.80^3 \]

### Step 3: Calculate \( 0.80^3 \)
Now, we need to calculate \( 0.80^3 \):
\[ 0.80^3 = 0.80 \times 0.80 \times 0.80 = 0.512 \]

### Step 4: Find the Depreciated Value
The value of the equipment after 3 years will be \( V \times 0.512 \).

### Step 5: Calculate How Much Less the Value is
To find out how much less the value is after 3 years, we can calculate:
\[ \text{Amount depreciated} = V - \text{Value after 3 years} = V - (V \times 0.512) = V \times (1 - 0.512) = V \times 0.488 \]

### Conclusion
Thus, the equipment will be worth \( V \times 0.488 \) less after 3 years.

### Final Answer
The value of the equipment will be **0.488 times less** after 3 years.

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