Chapter 9, Problem 37RE

a.

To determine

the salary during the fifth year of employment.

Answer to Problem 37RE

  $\$51,600$

Explanation of Solution

Concept Used:

The n^th term of an arithmetic sequence with first term $a_1$ and common difference d is given by:

  $a_n=a_1+\left(n-1\right)d$

Given problem represents an arithmetic sequence with first term $a_1=\$43,800$ and $d=\$1950$ .

Now the n^th term of this sequence is given by,

  $\begin{array}{c}{a}_n=a_1+\left(n-1\right)d\\ =43800+\left(n-1\right)\left(1950\right)\\ =43800+1950n-1950\\ =41850+1950n\end{array}$

The salary during the fifth year of employment is the fifth term of this sequence.

  $\begin{array}{c}{a}_5=41850+1950\left(5\right)\\ =41850+9750\\ =51,600\end{array}$

Conclusion:

The salary during the fifth year of employment is $51,600.

b.

To determine

the total compensation from the company through five full years of employment.

Answer to Problem 37RE

  $\$238,500$

Explanation of Solution

Concept Used:

The sum of first n terms of an arithmetic sequence with first term $a_1$ and last term $a_n$ is given by:

  $S_n=\frac{n}{2}\left(a_1+a_n\right)$

Given problem represents an arithmetic sequence with first term $a_1=\$43,800$ and $d=\$1950$ .

The total compensation from the company through five full years of employment is the sum of first 6 terms of this sequence which is given by:

  $\begin{array}{c}{S}_5=\frac{5}{2}\left(a_1+a_6\right)\\ =\frac{5}{2}\left(43,800+51,600\right)\\ =\frac{5}{2}\left(95,400\right)\\ =238,500\end{array}$

Conclusion:

The total compensation from the company through five full years of employment is $\$238,500$ .