The value of a car depreciates at the rate of 15% per annum. If its present value is Rs. 433500,what was the value in Rs. of the car 2 years ago?

Options

A. 594200
B. 620000
C. 563550
D. 600000

Answer

To find the value of the car 2 years ago given its present value and the rate of depreciation, we can follow these steps:

### Step 1: Understand the Depreciation Formula
The formula for calculating the present value (amount after depreciation) is:
\[ \text{Present Value} = \text{Principal} \times \left(1 - \frac{r}{100}\right)^t \]
where:
- \( r \) = rate of depreciation (15% in this case)
- \( t \) = time in years (2 years)
- Principal = value of the car 2 years ago

### Step 2: Substitute the Known Values
We know the present value is Rs. 433,500, the rate of depreciation is 15%, and the time is 2 years. We can substitute these values into the formula:
\[ 433500 = P \times \left(1 - \frac{15}{100}\right)^2 \]

### Step 3: Simplify the Equation
Calculate \( 1 - \frac{15}{100} \):
\[ 1 - \frac{15}{100} = 1 - 0.15 = 0.85 \]
Now, substitute this back into the equation:
\[ 433500 = P \times (0.85)^2 \]

### Step 4: Calculate \( (0.85)^2 \)
Calculate \( (0.85)^2 \):
\[ (0.85)^2 = 0.7225 \]
Now the equation becomes:
\[ 433500 = P \times 0.7225 \]

### Step 5: Solve for Principal (P)
To find the principal, rearrange the equation:
\[ P = \frac{433500}{0.7225} \]
Now, calculate \( P \):
\[ P = 600000 \]

### Conclusion
The value of the car 2 years ago was Rs. 600,000.