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The population of a village was 20,000 in the year 2019. It increased at the rate of 5% p.a. Find the population at the end of the year 2022.

Question

The population of a village was 20,000 in the year 2019. It increased at the rate of 5% p.a. Find the population at the end of the year 2022.

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Solution

To solve this problem, we need to apply the formula for compound interest, which is also used to calculate population growth. The formula is:

P = P0 * (1 + r/100)^n

where:

  • P is the final population
  • P0 is the initial population
  • r is the rate of increase (in this case, 5% per annum)
  • n is the number of years

Step 1: Identify the values from the problem:

  • P0 = 20,000 (the population in 2019)
  • r = 5% (the rate of increase per annum)
  • n = 2022 - 2019 = 3 years (the number of years from 2019 to 2022)

Step 2: Substitute the values into the formula:

P = 20000 * (1 + 5/100)^3

Step 3: Calculate the value:

P = 20000 * (1.05)^3 P = 20000 * 1.157625 P = 23152.5

So, the population at the end of the year 2022 would be approximately 23,153 (rounding up to the nearest whole number because we can't have a fraction of a person).

This problem has been solved

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