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In a company's first year in operation, it made an annual profit of
$391,500. The profit of the company increased at a constant
18% per year each year. How much total profit would the company make over the course of its first 6 years of operation, to the nearest whole number?
Answer:

In a company's first year in operation, it made an annual profit of $\$ 391,500$ . The profit of the company increased at a constant $18 \%$ per year each year. How much total profit would the company make over the course of its first $6$ years of operation, to the nearest whole number? $\newline$ Answer:

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Exponential growth and decay: word problems

Full solution

Q. In a company's first year in operation, it made an annual profit of

\$ 391,500

. The profit of the company increased at a constant

18 \%

per year each year. How much total profit would the company make over the course of its first

6

years of operation, to the nearest whole number?

\newline

Answer:

Identify Initial Profit: Identify the initial profit and the annual increase rate. $\newline$ The initial profit is $\$391,500$ , and the profit increases by $18\%$ each year.
Calculate Yearly Profits: Calculate the profit for each year using the formula for compound interest: $P = P_0 \times (1 + r)^n$ , where $P_0$ is the initial amount, $r$ is the rate of increase, and $n$ is the number of years. $\newline$ Year $1$ : $P = \$391,500$ $\newline$ Year $2$ : $P = \$391,500 \times (1 + 0.18)^1$ $\newline$ Year $3$ : $P = \$391,500 \times (1 + 0.18)^2$ $\newline$ Year $4$ : $P = \$391,500 \times (1 + 0.18)^3$ $\newline$ Year $5$ : $P = \$391,500 \times (1 + 0.18)^4$ $\newline$ Year $6$ : $P = \$391,500 \times (1 + 0.18)^5$
Calculate Individual Profits: Calculate the profit for each year. $\newline$ Year $2$ : $P = \$391,500 \times 1.18 = \$462,170$ $\newline$ Year $3$ : $P = \$391,500 \times (1.18)^2 = \$545,360.60$ $\newline$ Year $4$ : $P = \$391,500 \times (1.18)^3 = \$643,525.51$ $\newline$ Year $5$ : $P = \$391,500 \times (1.18)^4 = \$759,360.50$ $\newline$ Year $6$ : $P = \$391,500 \times (1.18)^5 = \$896,045.39$
Calculate Total Profit: Add up the profits for each year to get the total profit over $6$ years. $\newline$ Total Profit = Year $1$ + Year $2$ + Year $3$ + Year $4$ + Year $5$ + Year $6$ $\newline$ Total Profit = $\$391,500$ + $\$462,170$ + $\$545,360.60$ + $\$643,525.51$ + $\$759,360.50$ + $\$896,045.39$
Perform Addition: Perform the addition to find the total profit. $\newline$ Total Profit = $\$391,500 + \$462,170 + \$545,360.60 + \$643,525.51 + \$759,360.50 + \$896,045.39 = \$3,697,962$

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