The value of a machine, purchased two years ago, depreciates at the annual rate of 10%. If its present value is Rs 97,200, find it value after 2 years

Answer

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

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Present Value (PV) = Rs 97,200
- Rate of Depreciation (R) = 10% (as it is depreciation, we will consider it as -10%)
- Time (T) = 2 years

2. **Understand the Formula:**
The formula for calculating the future value (A) after depreciation is:
\[ A = P \times \left(1 + \frac{R}{100}\right)^T \]
Where:
- A = Future Value
- P = Present Value (Principal)
- R = Rate of Depreciation
- T = Time in years

3. **Substitute the Values into the Formula:**
Since the rate is negative due to depreciation, we will use:
\[ A = 97200 \times \left(1 - \frac{10}{100}\right)^2 \]
Simplifying the expression inside the parentheses:
\[ A = 97200 \times \left(1 - 0.10\right)^2 \]
\[ A = 97200 \times (0.90)^2 \]

4. **Calculate (0.90)^2:**
\[ (0.90)^2 = 0.81 \]

5. **Multiply the Present Value by the Result:**
\[ A = 97200 \times 0.81 \]

6. **Perform the Multiplication:**
\[ A = 97200 \times 0.81 = 78,732 \]

7. **Conclusion:**
The value of the machine after 2 years is Rs 78,732.