Question : The population of a town increased from 100000 to 250000 in 5 years. What is the approximate compounded percent increase in population per year?
Option 1: 20 percent
Option 2: 30 percent
Option 3: 10 percent
Option 4: 40 percent
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Correct Answer: 20 percent
Solution :
Here, the initial population was 100,000 and the final population was 250,000.
So, compound interest = 250000 – 100000 = 150000
Time = 5 years
Let the rate of interest be $r$.
We know, $\text{Compound interest}=\text{Principal}×(1+\frac{\text{Rate}}{100})^{\text{Time}}-\text{Principal}$
$⇒150000=100000(1+\frac{r}{100})^5-100000$
$⇒(1+\frac{r}{100})^5=\frac{250000}{100000}$
$⇒(1+\frac{r}{100})^5=(\frac{12}{10})^5$ [$\because \sqrt[5]{250000}\approx 12$]
$⇒1+\frac{r}{100}=\frac{12}{10}$
$⇒r=20\%$
Hence, the correct answer is 20 percent.
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