The value of a machine depreciates `10%` annually. If its present value is Rs. 4000. Its value 2 years hence will be-

Options

A. Rs. 3200
B. Rs. 3240
C. Rs. 3260
D. Rs. 3280

Answer

To find the value of a machine that depreciates by 10% annually, we can follow these steps:

### Step 1: Understand the depreciation formula
The value of an asset after depreciation can be calculated using the formula:
\[ \text{Future Value} = \text{Present Value} \times (1 - \text{Depreciation Rate})^n \]
where:
- Present Value = Current value of the asset
- Depreciation Rate = Rate of depreciation (in decimal)
- \( n \) = Number of years

### Step 2: Identify the values
From the problem:
- Present Value = Rs. 4000
- Depreciation Rate = 10% = 0.10
- \( n = 2 \) years

### Step 3: Substitute the values into the formula
Now, we can substitute the values into the formula:
\[ \text{Future Value} = 4000 \times (1 - 0.10)^2 \]

### Step 4: Calculate the depreciation factor
Calculate \( (1 - 0.10) \):
\[ 1 - 0.10 = 0.90 \]

### Step 5: Raise the depreciation factor to the power of \( n \)
Now, raise \( 0.90 \) to the power of \( 2 \):
\[ 0.90^2 = 0.81 \]

### Step 6: Calculate the future value
Now, multiply the present value by the depreciation factor:
\[ \text{Future Value} = 4000 \times 0.81 = 3240 \]

### Final Answer
The value of the machine 2 years hence will be Rs. 3240.

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