in a companys first year in operation, it made an annual profit of $416,500. the profit of the company…

in a companys first year in operation, it made an annual profit of $416,500. the profit of the company increased at a constant 28% per year each year. how much total profit would the company make over the course of its first 10 years of operation, to the nearest whole number?

in a companys first year in operation, it made an annual profit of $416,500. the profit of the company increased at a constant 28% per year each year. how much total profit would the company make over the course of its first 10 years of operation, to the nearest whole number?

Answer

Explanation:

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

The sum of a geometric series $S_n=\frac{a(1 - r^n)}{1 - r}$, where $a$ is the first - term, $r$ is the common ratio, and $n$ is the number of terms. Here, $a = 416500$, $r=1 + 0.28=1.28$, and $n = 10$.

Step2: Substitute the values into the formula

$S_{10}=\frac{416500(1 - 1.28^{10})}{1 - 1.28}$. First, calculate $1.28^{10}$. Using a calculator, $1.28^{10}\approx15.46763$. Then, $1-1.28^{10}=1 - 15.46763=-14.46763$. And $1 - r=1 - 1.28=-0.28$. So, $S_{10}=\frac{416500\times(- 14.46763)}{-0.28}$. $S_{10}=\frac{-6025777.895}{-0.28}\approx21520635$.

Answer:

$21520635$