The value of a machine dereciates at the rate of 10% per annum. It was purchased 3 years ago for 60000. What is the present value of the machine?

Options

A. Rs 53640
B. Rs 51680
C. Rs 43740
D. Rs 43470

Answer

To find the present value of the machine that depreciates at a rate of 10% per annum, we can follow these steps:

### Step 1: Identify the given values
- **Initial Value (Principal)** = ₹60,000
- **Rate of Depreciation** = 10% per annum
- **Time (n)** = 3 years

### Step 2: Write the formula for present value considering depreciation
The formula for calculating the present value when depreciation occurs is:

\[ \text{Present Value} = \text{Principal} \times \left(1 - \frac{\text{Rate}}{100}\right)^n \]

### Step 3: Substitute the known values into the formula
Substituting the values we have into the formula:

\[ \text{Present Value} = 60000 \times \left(1 - \frac{10}{100}\right)^3 \]

### Step 4: Simplify the expression inside the parentheses
Calculate \(1 - \frac{10}{100}\):

\[ 1 - \frac{10}{100} = 1 - 0.10 = 0.90 \]

### Step 5: Raise the result to the power of n (3 years)
Now, we need to calculate \(0.90^3\):

\[ 0.90^3 = 0.90 \times 0.90 \times 0.90 = 0.729 \]

### Step 6: Multiply by the initial value
Now, multiply this result by the initial value:

\[ \text{Present Value} = 60000 \times 0.729 \]

### Step 7: Calculate the final present value
Calculating the multiplication:

\[ \text{Present Value} = 60000 \times 0.729 = 43740 \]

### Conclusion
The present value of the machine after 3 years is ₹43,740.

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