The population of a town 2 years ago was `62,500`. Due to migration to cities it decreases every year at the rate of 4% per annum. Find its present population.

Options

A. 56700
B. 45000
C. 50000
D. 57600

Answer

To find the present population of the town, we will use the formula for compound interest, which can also be applied to population decrease. The formula is:

\[ P = P_0 \times (1 - \frac{r}{100})^n \]

Where:
- \( P \) is the present population,
- \( P_0 \) is the initial population (2 years ago),
- \( r \) is the rate of decrease (in percentage),
- \( n \) is the number of years.

### Step-by-Step Solution:

1. **Identify the given values**:
- Initial population \( P_0 = 62,500 \)
- Rate of decrease \( r = 4\% \)
- Number of years \( n = 2 \)

2. **Substitute the values into the formula**:
\[ P = 62,500 \times \left(1 - \frac{4}{100}\right)^2 \]

3. **Calculate \( 1 - \frac{4}{100} \)**:
\[ 1 - \frac{4}{100} = 1 - 0.04 = 0.96 \]

4. **Substitute back into the equation**:
\[ P = 62,500 \times (0.96)^2 \]

5. **Calculate \( (0.96)^2 \)**:
\[ (0.96)^2 = 0.9216 \]

6. **Multiply the initial population by \( 0.9216 \)**:
\[ P = 62,500 \times 0.9216 \]

7. **Perform the multiplication**:
\[ P = 57,600 \]

### Final Result:
The present population of the town is **57,600**.

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