A manufacture reckons that the value of a machine which costs him Rs. 156250, will depreciate each year by 20%. Find the estimated value at the end of 5 years.

Answer

To find the estimated value of a machine after 5 years, given that it depreciates by 20% each year, we can use the formula for depreciation:

\[ A = P \left(1 - \frac{r}{100}\right)^t \]

Where:
- \( A \) is the estimated value after \( t \) years,
- \( P \) is the initial value (cost of the machine),
- \( r \) is the rate of depreciation,
- \( t \) is the number of years.

### Step-by-Step Solution:

1. **Identify the values**:
- Initial cost of the machine, \( P = 156250 \) Rs.
- Rate of depreciation, \( r = 20\% \).
- Time period, \( t = 5 \) years.

2. **Substitute the values into the formula**:
\[ A = 156250 \left(1 - \frac{20}{100}\right)^5 \]

3. **Calculate \( 1 - \frac{20}{100} \)**:
\[ 1 - \frac{20}{100} = 1 - 0.2 = 0.8 \]

4. **Substitute back into the formula**:
\[ A = 156250 \times (0.8)^5 \]

5. **Calculate \( (0.8)^5 \)**:
\[ (0.8)^5 = 0.32768 \]

6. **Multiply by the initial cost**:
\[ A = 156250 \times 0.32768 \]

7. **Perform the multiplication**:
\[ A = 51200 \]

### Final Result:
The estimated value of the machine at the end of 5 years is **Rs. 51200**.

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