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Interactive Examples
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Question 3
The population of a country that you want to sell your product to is increasing at a rate of 5% per year. If the population is currently 7,000,000, what will be the population in 12 years?
7000000 * (1 + .05)^12
To find the population in 12 years, we need to use the formula for compound interest. In this case, the population growth can be thought of as compound interest, where the initial population is the principal, the growth rate is the interest rate, and the number of years is the time period.
The formula for compound interest is: A = P(1 + r/n)^(nt), where:
- A is the final amount (population in this case)
- P is the principal (initial population)
- r is the interest rate (growth rate)
- n is the number of times the interest is compounded per year (assume it's compounded annually)
- t is the number of years
In this scenario, the formula becomes: A = P(1 + r)^t
Let's substitute the given values into the formula and calculate the population in 12 years.
P = 7,000,000 (initial population)
r = 5% (growth rate per year expressed as a decimal, so 5% = 0.05)
t = 12 (number of years)
A = 7,000,000 * (1 + 0.05)^12
Now, let's calculate the population:
A = 7,000,000 * (1.05)^12
To evaluate this expression, you can use a calculator or do it step by step:
1.05^2 = 1.1025
1.1025^2 = 1.21550625
1.21550625^2 = 1.3632256
1.3632256^2 = 1.6464169
1.6464169^2 = 2.70727565
A = 7,000,000 * 2.70727565
A = 18,950,929.5
Therefore, the population of the country in 12 years will be approximately 18,950,930.