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.

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).