Jadeja purchased a maruti car 3 years ago for Rs.2 lakh . Its value depreciated each year @ 25% p.a. What is the present value of the car ?

Answer

To find the present value of Jadeja's car after 3 years of depreciation at a rate of 25% per annum, we can follow these steps:

### Step 1: Identify the initial value and depreciation rate
- The initial value (Principal, P) of the car is Rs. 2,00,000.
- The depreciation rate (R) is 25% per annum.
- The time period (T) is 3 years.

### Step 2: Calculate the depreciation factor
Since the car depreciates at a rate of 25% per annum, the remaining value after each year can be calculated using the formula:
\[ \text{Remaining Value} = P \times (1 - \frac{R}{100})^T \]

Substituting the values:
\[ \text{Remaining Value} = 2,00,000 \times (1 - \frac{25}{100})^3 \]
\[ = 2,00,000 \times (0.75)^3 \]

### Step 3: Calculate \( (0.75)^3 \)
Now, we need to calculate \( (0.75)^3 \):
\[ (0.75)^3 = 0.75 \times 0.75 \times 0.75 = 0.421875 \]

### Step 4: Calculate the present value
Now, substitute \( (0.75)^3 \) back into the equation:
\[ \text{Remaining Value} = 2,00,000 \times 0.421875 \]
\[ = 84,375 \]

### Conclusion
The present value of the car after 3 years of depreciation is Rs. 84,375.

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