Chapter 8.4, Problem 18E

To determine

Find the total profit of the company using given statement.

Answer to Problem 18E

Thetotal profits of the company are $\$291,6667$ .

Explanation of Solution

Given:

The given statement is that the first year profit of the company is $\$3,50,000$ and the profit decreased by $12\%$ per year.

Calculation:

The statement shows the geometric series.

  $350000+350000\left(0.88\right)+350000{\left(0.88\right)}^2+\cdot \cdot \cdot$

The sum of an infinite geometric series with first term $a_1$ and common ratio $r$ is

  $S=\frac{a_1}{1-r}$ , where $r<1$ .

If $r\ge 1$ , then the series has no sum.

In the given series $a_1=350000$ and $r=0.88<1$ .

  $\begin{array}{l}S=\frac{350000}{1-0.88}\\ =\frac{350000}{0.12}\\ =2916667\end{array}$

Hence the total profits of the company are $\$291,6667$ .