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

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

Explanation:

Use geometric sum formula:

`S_n=(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)=(242500(1-1.22^(30)))/(1-1.22)=\$428,517,224 \ \textsf{(nearest whole number)}`