Question

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 1

Answer:

total profit = $428,517,224  (nearest whole number)

Step-by-step explanation:

Use geometric sum formula:

$S_n=\dfrac{a(1-r^n)}{1-r}$

where $a$ is the initial value and $r$ is the common ratio

We have been told that the initial value is 242500, so $a=242500$.

If the company's profit increases by 22% per year, this means each year's profit is 122% of the previous year's profit. 122% = 122/100 = 1.22

Therefore, $r = 1.22$

We need to calculate the total profit earned over 30 years, so $n = 30$

Inputting these values into the formula:

$\implies S_{30}=\dfrac{242500(1-1.22^{30})}{1-1.22}=\ 428,517,224 \ \textsf{(nearest whole number)}$