Question

In a company's first year in operation, it made an annual profit of $171,000. The profit of the company increased at a constant 33% per year each year. How much total profit would the company make over the course of its first 29 years of operation, to the nearest whole number?

Answer 1

total profit = $2,023,338,517 (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 171000, so
`a=171000`.

If the company's profit increases by 33% per year, this means each year's profit is 133% of the previous year's profit. 133% = 133/100 = 1.33

Therefore,
`r = 1.33`

We need to calculate the total profit earned over 29 years, so
`n = 29`

Inputting these values into the formula:

`\implies S_(29)=(171000(1-1.33^(29)))/(1-1.33)=\$2,023,338,517 \ \textsf{(nearest whole number)}`