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The population of village increases at the rate of 6% per annum. There is an additional increase of 2% in the population due to rural development .Therefore the percentage increase in the population after 2 years will be:
- a)15.46%
- b)16.64%
- c)14.46%
- d)12.56%
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
The population of village increases at the rate of 6% per annum. There...
Total increase = 6+2 = 8%
% increase = 8+8+(8*8/100) = 16+0.64 = 16.64%
% increase = 8+8+(8*8/100) = 16+0.64 = 16.64%
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The population of village increases at the rate of 6% per annum. There...
Population Increase Calculation:
The population of the village increases at a rate of 6% per annum. This means that the population will increase by 6% every year.
Additional Increase due to Rural Development:
In addition to the 6% increase, there is an additional increase of 2% in the population due to rural development. This means that the total population increase will be 6% (existing growth rate) + 2% (additional increase) = 8%.
Percentage Increase in Population after 2 years:
To calculate the percentage increase in the population after 2 years, we need to consider compounding of the growth rates. The formula for compound interest is A = P(1 + r/n)^(nt), where:
- A is the final amount
- P is the initial principal balance
- r is the interest rate
- n is the number of times that interest is compounded per year
- t is the number of years
In this case, P = 100 (considering initial population as 100 for easy calculation), r = 8% (6% + 2%), n = 1 (compounded annually), and t = 2 years.
Plugging in the values into the formula:
A = 100(1 + 0.08)^(1*2)
A = 100(1.08)^2
A = 100(1.1664)
A = 116.64
Percentage Increase:
The percentage increase in population after 2 years can be calculated using the formula: Percentage Increase = (Final Population - Initial Population) / Initial Population * 100
Percentage Increase = (116.64 - 100) / 100 * 100
Percentage Increase = 16.64%
Therefore, the percentage increase in the population after 2 years will be 16.64% (option B).
The population of the village increases at a rate of 6% per annum. This means that the population will increase by 6% every year.
Additional Increase due to Rural Development:
In addition to the 6% increase, there is an additional increase of 2% in the population due to rural development. This means that the total population increase will be 6% (existing growth rate) + 2% (additional increase) = 8%.
Percentage Increase in Population after 2 years:
To calculate the percentage increase in the population after 2 years, we need to consider compounding of the growth rates. The formula for compound interest is A = P(1 + r/n)^(nt), where:
- A is the final amount
- P is the initial principal balance
- r is the interest rate
- n is the number of times that interest is compounded per year
- t is the number of years
In this case, P = 100 (considering initial population as 100 for easy calculation), r = 8% (6% + 2%), n = 1 (compounded annually), and t = 2 years.
Plugging in the values into the formula:
A = 100(1 + 0.08)^(1*2)
A = 100(1.08)^2
A = 100(1.1664)
A = 116.64
Percentage Increase:
The percentage increase in population after 2 years can be calculated using the formula: Percentage Increase = (Final Population - Initial Population) / Initial Population * 100
Percentage Increase = (116.64 - 100) / 100 * 100
Percentage Increase = 16.64%
Therefore, the percentage increase in the population after 2 years will be 16.64% (option B).
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The population of village increases at the rate of 6% per annum. There is an additional increase of 2% in the population due to rural development .Therefore the percentage increase in the population after 2 years will be:a)15.46%b)16.64%c)14.46%d)12.56%Correct answer is option 'B'. Can you explain this answer?
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