A scooter is bought for Rs 32000. Its value depreclates at 10% per annum. What will be Its value after 2 years?

Answer

To find the value of the scooter after 2 years, given that its value depreciates at a rate of 10% per annum, we can use the formula for compound depreciation. Here’s the step-by-step solution:

### Step 1: Identify the initial values
- **Principal (P)**: Rs 32,000 (the initial value of the scooter)
- **Rate of depreciation (r)**: 10% per annum
- **Time (n)**: 2 years

### Step 2: Write the formula for compound depreciation
The formula for calculating the amount after depreciation is:
\[ A = P \times \left(1 - \frac{r}{100}\right)^n \]
Where:
- \( A \) is the amount after \( n \) years,
- \( P \) is the principal amount,
- \( r \) is the rate of depreciation,
- \( n \) is the number of years.

### Step 3: Substitute the values into the formula
Substituting the known values into the formula:
\[ A = 32000 \times \left(1 - \frac{10}{100}\right)^2 \]

### Step 4: Simplify the expression inside the brackets
Calculate \( 1 - \frac{10}{100} \):
\[ 1 - \frac{10}{100} = 1 - 0.1 = 0.9 \]
So, we can rewrite the equation as:
\[ A = 32000 \times (0.9)^2 \]

### Step 5: Calculate \( (0.9)^2 \)
Now calculate \( (0.9)^2 \):
\[ (0.9)^2 = 0.81 \]
Thus, the equation becomes:
\[ A = 32000 \times 0.81 \]

### Step 6: Multiply to find the final amount
Now perform the multiplication:
\[ A = 32000 \times 0.81 = 25920 \]

### Step 7: State the final value
Therefore, the value of the scooter after 2 years is:
\[ \text{Value after 2 years} = Rs 25,920 \]

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