in a companys first year in operation, it made an annual profit of $242,500. the profit of the company…

in a companys first year in operation, it made an annual profit of $242,500. the profit of the company increased at a constant 22% per year each year. how much total profit would the company make over the course of its first 30 years of operation, to the nearest whole number?

in a companys first year in operation, it made an annual profit of $242,500. the profit of the company increased at a constant 22% per year each year. how much total profit would the company make over the course of its first 30 years of operation, to the nearest whole number?

Answer

Explanation:

Step1: Identify the formula for the sum of a geometric - series

The profit forms a geometric series with first - term $a = 242500$ and common ratio $r=1 + 0.22=1.22$. The sum of the first $n$ terms of a geometric series is given by $S_n=\frac{a(r^n - 1)}{r - 1}$ when $r\neq1$.

Step2: Substitute the values into the formula

Here, $a = 242500$, $r = 1.22$, and $n = 30$. So, $S_{30}=\frac{242500\times(1.22^{30}-1)}{1.22 - 1}$.

Step3: Calculate $1.22^{30}$

Using a calculator, $1.22^{30}\approx339.8494$.

Step4: Calculate the numerator

$1.22^{30}-1\approx339.8494 - 1=338.8494$. Then, $242500\times(1.22^{30}-1)=242500\times338.8494\approx82170979.5$.

Step5: Calculate the denominator

$r - 1=1.22-1 = 0.22$.

Step6: Calculate the sum

$S_{30}=\frac{82170979.5}{0.22}\approx373504452$.

Answer:

$373504452$