Solving an Application Problem with a Geometric Series

At a new job, an employee’s starting salary is $26,750. He receives a 1.6% annual raise. Find his total earnings at the end of 5 years.

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
The problem can be represented by a geometric series with $a_{1} = 26, 750;$ $n = 5;$ and $r = 1.016.$ Substitute values for $a_{1},$ $r,$ and $n$ into the formula and simplify to find the total amount earned at the end of 5 years.
$\begin{array}{l} S_{n} = \frac{a_{1} (1 - r^{n})}{1 - r} \\ S_{5} = \frac{26, 750 (1 - {1.016}^{5})}{1 - 1.016} \approx 138, 099.03 \end{array}$
He will have earned a total of $138,099.03 by the end of 5 years.

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

At a new job, an employee’s starting salary is $32,100. She receives a 2% annual raise. How much will she have earned by the end of 8 years?

How did it go?