If the value of a machine is RS P and it depreciates at R% per annum, then its value after 2 years is ………

Options

A. Rs ` P(1-(R)/(100))^3`
B. `Rs P(1-(R)/(100))^2`
C. `Rs P(1-(R)/(200))^2`
D. `Rs P(1-(R)/(400))^4`

Answer

To find the value of a machine after 2 years of depreciation at a rate of R% per annum, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Let the initial value of the machine be \( P \) (in Rs).
- The rate of depreciation is \( R\% \) per annum.
- The time period is \( 2 \) years.

2. **Understand the Concept of Depreciation:**
- Depreciation means the value of the machine decreases over time.
- Since it is compounded annually, we will use the formula for compound interest, but we will adjust it for depreciation.

3. **Use the Formula for Depreciation:**
- The formula for the amount after depreciation is:
\[ A = P \times \left(1 - \frac{R}{100}\right)^n \]
- Here, \( A \) is the amount after \( n \) years, \( P \) is the principal amount, \( R \) is the rate of depreciation, and \( n \) is the number of years.

4. **Substitute the Values into the Formula:**
- Substitute \( P \) for the principal, \( R \) for the rate, and \( 2 \) for \( n \):
\[ A = P \times \left(1 - \frac{R}{100}\right)^2 \]

5. **Final Expression:**
- Therefore, the value of the machine after 2 years is:
\[ A = P \times \left(1 - \frac{R}{100}\right)^2 \]

### Final Answer:
The value of the machine after 2 years is \( P \times \left(1 - \frac{R}{100}\right)^2 \).

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