Chapter 8, Problem 43RE

(a)

To determine

To find the salary during the fifth year −

Starting Salary − $\$53,300$

Guaranteed Salary Increase per year - $\$1,066$

Answer to Problem 43RE

Thesalary during the fifth year is $\$57,564$ .

Explanation of Solution

Given:

Starting Salary − $\$53,300$

Guaranteed Salary Increase per year - $\$1,066$

Formula Used:

  $nth$ term for an ArithmeticSequence is $t_n=a+\left(n-1\right)d$

Calculation:

Salary during the fifth year is given as:

  $\begin{array}{l}{t}_5=53300+\left(5-1\right)1066\\ t_5=57564\end{array}$

Conclusion:

Hence, the salary during the fifth year is $\$57,564$ .

(b)

To determine

To find the salary during the fifth year −

Starting Salary − $\$53,300$

Guaranteed Salary Increase per year - $\$1,066$

Answer to Problem 43RE

Total compensation through $5$ full years is $\$277,160$ .

Explanation of Solution

Given:

Starting Salary − $\$53,300$

Guaranteed Salary Increase per year - $\$1,066$

Formula Used:

Sum of an Arithmetic Sequence: $S_n=\frac{n}{2}\left[2a+\left(n-1\right)d\right]$

Calculation:

Total compensation through $5$ full years is given as:

  $\begin{array}{l}{S}_5=\frac{5}{2}\left[2\left(53300\right)+\left(5-1\right)1066\right]\\ S_5=\frac{5}{2}\left(106600+4264\right)\\ S_5=\frac{5}{2}\left(110864\right)\\ S_5=277160\end{array}$

Conclusion:

Hence, the salary during the fifth year is $\$277,160$ .