The price of motorcycle depreciates every year by 8%. If the value of the motorcycle after 2 years will be Rs. 84640, then what is the present value (in Rs.) of the motorcycle?

Options

A. 90000
B. 102000
C. 110000
D. 100000

Answer

To find the present value of the motorcycle given its depreciated value after 2 years, we can follow these steps:

### Step 1: Understand the depreciation
The motorcycle depreciates by 8% each year. This means that after one year, the value of the motorcycle will be 92% of its value at the beginning of that year (100% - 8% = 92%).

### Step 2: Calculate the depreciation factor
The depreciation factor can be expressed as:
\[ \text{Depreciation Factor} = 1 - \frac{8}{100} = 0.92 \]

### Step 3: Apply the depreciation over 2 years
After 2 years, the value of the motorcycle can be calculated using the formula:
\[ \text{Value after 2 years} = \text{Present Value} \times (\text{Depreciation Factor})^2 \]
Substituting the depreciation factor:
\[ \text{Value after 2 years} = \text{Present Value} \times (0.92)^2 \]

### Step 4: Plug in the known value
We know that the value of the motorcycle after 2 years is Rs. 84,640. Therefore, we can set up the equation:
\[ 84640 = \text{Present Value} \times (0.92)^2 \]

### Step 5: Calculate \( (0.92)^2 \)
Calculating \( (0.92)^2 \):
\[ (0.92)^2 = 0.8464 \]

### Step 6: Substitute back into the equation
Now we can substitute this value back into the equation:
\[ 84640 = \text{Present Value} \times 0.8464 \]

### Step 7: Solve for Present Value
To find the Present Value, we rearrange the equation:
\[ \text{Present Value} = \frac{84640}{0.8464} \]

### Step 8: Perform the division
Calculating the division:
\[ \text{Present Value} = 100000 \]

### Conclusion
The present value of the motorcycle is Rs. 100,000.

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