Chapter 11.3, Problem 2P

To determine

To calculate:

The salary amount of third year.

Answer to Problem 2P

The salary amount of third year is $\$16,224$ .

Explanation of Solution

Given information:

Starting salary: $\$15,000$

Annual raises: $4\%=0.04$

Formula used:

  $a\left(n\right)=a\left(1\right)+d\left(n-1\right)$

Where,

  $a\left(1\right)$ = first term of arithmetic sequence

  $d=$ common difference of the arithmetic sequence.

  $n=$ indicated term

Calculation:

First, identify the first term of the arithmetic sequence such as the initial salary,

  $a\left(1\right)=\$15,000$

Then consider the common difference of the arithmetic sequence, the amount pay will change in each year.

  $d=0.04$

Now, identify the indicated term of the sequence, the year in which about to know the salary.

  $n=3$

So, by using all of the this the given equation is

  $a\left(3\right)=15000+0.04\left(3-1\right)$

During first year on the job, salary is $\$15000$

During second year on the job, salary is $\$15000\times 1.04=\$15,600$

During third year on the job, salary is $\$15,600\times 1.04=\$16,224.$

That’s $\$15000\times {1.04}^2.$

This assumes that the raises are given at the end of each year on the job.

So, the salary if the third year is $\$16,224$ .