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

in a company’s 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 company’s 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 series type

This is a geometric series problem where the first term (a = 242500), the common ratio (r=1 + 0.22=1.22), and the number of terms (n = 30). The formula for the sum of a geometric series is (S_n=\frac{a(r^n - 1)}{r - 1}) (when (r\neq1)).

Step2: Substitute values into the formula

Substitute (a = 242500), (r = 1.22), and (n = 30) into the sum formula: [S_{30}=\frac{242500\times(1.22^{30}-1)}{1.22 - 1}]

Step3: Calculate (1.22^{30})

Using a calculator, (1.22^{30}\approx349.38)

Step4: Calculate the numerator

First, calculate (1.22^{30}-1\approx349.38 - 1 = 348.38) Then, multiply by (a): (242500\times348.38\approx242500\times348.38 = 84482150)

Step5: Calculate the denominator

The denominator is (1.22 - 1=0.22)

Step6: Calculate the sum

Divide the numerator by the denominator: (\frac{84482150}{0.22}\approx384009772.73)

Answer:

(384009773) (rounded to the nearest whole number)