The value of a machine depreciates at the rate of 10% per year. It was purchased 3 yr ago. If its present value is Rs.145800 for how much was it purchased?

Options

A. Rs.175800
B. Rs.180000
C. Rs.200000
D. Rs.210000

Answer

To find the initial purchase price of the machine, we can use the formula for depreciation. The formula for the present value (PV) after depreciation is given by:

\[ PV = \text{Initial Value} \times (1 - r)^t \]

Where:
- \( PV \) is the present value of the machine (Rs. 145800),
- \( r \) is the rate of depreciation (10% or 0.10),
- \( t \) is the time in years (3 years).

We need to rearrange this formula to find the Initial Value (IV):

\[ \text{Initial Value} = \frac{PV}{(1 - r)^t} \]

### Step 1: Substitute the known values into the formula

Substituting the values we have:

- \( PV = 145800 \)
- \( r = 0.10 \)
- \( t = 3 \)

So, we have:

\[ \text{Initial Value} = \frac{145800}{(1 - 0.10)^3} \]

### Step 2: Calculate \( (1 - r) \)

First, calculate \( (1 - r) \):

\[ 1 - 0.10 = 0.90 \]

### Step 3: Raise \( 0.90 \) to the power of \( 3 \)

Now, calculate \( (0.90)^3 \):

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

### Step 4: Substitute this value back into the formula

Now substitute back into the formula for Initial Value:

\[ \text{Initial Value} = \frac{145800}{0.729} \]

### Step 5: Perform the division

Now, perform the division:

\[ \text{Initial Value} = 199,452.05 \]

### Conclusion

Thus, the initial purchase price of the machine was approximately Rs. 199,452.05.

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