Question

The population of a town is 2,24,375. If it increases at the rate of 4% per annum, what will be its population 2 years hence?

• A. 2,42,684
• B. 2,40,468
• C. 2,36,864
• D. 2,32,846

Answer 1

Answer:

A. 2,42,684

The population of the town 2 years hence will be 2,42,684.

To find the future population, we use the formula for compound interest:
$A = P \times \left(1 + \frac{R}{100}\right)^n$

Where:

• $P$ (Initial Population) = 2,24,375

• $R$ (Growth Rate) = 4% per annum

• $n$ (Time Period) = 2 years

• $A$ (Future Population) = Population after 2 years

Method 1: Using the Formula

1. Substitute the values into the formula:
   $A = 2,24,375 \times \left(1 + \frac{4}{100}\right)^2$

2. Simplify the term inside the bracket:
   $A = 2,24,375 \times (1.04)^2$

3. Square the growth factor:
   $A = 2,24,375 \times 1.0816$

4. Calculate the final value:
   $A = 2,42,684$

Method 2: Year-by-Year Calculation

• Population after 1 year:
  $2,24,375 + (4\% \text{ of } 2,24,375) = 2,24,375 + 8,975 = 2,33,350$

• Population after 2 years:
  $2,33,350 + (4\% \text{ of } 2,33,350) = 2,33,350 + 9,334 = 2,42,684$