Question : 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?
Option 1: 562432
Option 2: 652432
Option 3: 465223
Option 4: 564232
Correct Answer: 562432
Solution :
The population after $n$ years can be calculated by using the formula $P(1+\frac{\text{R}}{100})^n$ where $P$ is the initial value, $R$ is the rate and $n$ is the time.
The population on 1
st
January 2001 was 500000.
Population after 3 years
$= 500000(1+\frac{4}{100})^3$
$= 500000(1+\frac{1}{25})^3$
$= 500000(\frac{26}{25})^3$
$= 500000 \times \frac{26}{25}\times \frac{26}{25}\times \frac{26}{25}$
$= 562432$
Hence, the correct answer is 562432.
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