The population of a town increases each year by 4% of its total at the beginning of the year. If the population on 1st January 2001 was 500000, what was it on 1st January, 2004?

Options

A. 562432
B. 652432
C. 465223
D. 564232

Answer

To find the population of the town on 1st January 2004, we will calculate the population for each year from 2001 to 2004, taking into account the annual increase of 4%.

### Step-by-Step Solution:

1. **Initial Population (2001)**:
- The population on 1st January 2001 is given as 500,000.

2. **Calculate Population for 2002**:
- The population increases by 4% each year.
- Increase for 2002 = 4% of 500,000 = (4/100) * 500,000 = 20,000.
- Population on 1st January 2002 = 500,000 + 20,000 = 520,000.

3. **Calculate Population for 2003**:
- Now, we calculate the increase for 2003 based on the population at the beginning of 2002.
- Increase for 2003 = 4% of 520,000 = (4/100) * 520,000 = 20,800.
- Population on 1st January 2003 = 520,000 + 20,800 = 540,800.

4. **Calculate Population for 2004**:
- Now, we calculate the increase for 2004 based on the population at the beginning of 2003.
- Increase for 2004 = 4% of 540,800 = (4/100) * 540,800 = 21,632.
- Population on 1st January 2004 = 540,800 + 21,632 = 562,432.

### Final Answer:
The population of the town on 1st January 2004 is **562,432**.