Chapter 11.5, Problem 9P

a.

To determine

To calculate:

Total amount Job A will pay.

Answer to Problem 9P

Total amount Job A will pay is $\$26000$ .

Explanation of Solution

Given information:

Annual subscription cost: $\$20,000$

Cost raises: $\$1500$

Formula used:

  $a_n=a_1+d\left(n-1\right)$

Where,

  $a_1=$ = 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,

  $a_1=\$20,000$

Then consider the common difference of the arithmetic sequence,

  $d=\$1500$

Now, identify the indicated term of the sequence,

  $n=5$

So, by using all of this the given equation is

  $\begin{array}{l}{a}_5=20000+1500\left(5-1\right)\\ a_5=26000\end{array}$

Therefore, total amount Job A will pay is $\$26000$ .

b.

To determine

To calculate:

Total amount Job B will pay.

Answer to Problem 9P

Total amount Job B will pay is $\$20000$ .

Explanation of Solution

Given information:

Annual subscription cost: $\$18000$

Cost rises: $10\%=0.1$

Formula used:

  $a_n=\frac{a_1\left(1-r^n\right)}{1-r}$

Where,

  $a_1=$ = First term of geometric sequence

  $r=$ Common ratio of the geometric sequence.

  $n=$ Indicated term

Calculation:

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

  $a_1=\$18000$

Then consider the common ratio of the geometric sequence,

  $r=0.1$

Now, identify the indicated term of the sequence,

  $n=5$

So, by using all of this the given equation is

  $\begin{array}{l}{a}_5=\frac{a_1\left(1-r^n\right)}{1-r}\\ a_5=\frac{18000\left({1.1}^{0.1}\right)}{1-0.1}\\ a_5=\frac{18000\left(1\right)}{1-0.1}\\ a_5=\frac{18000}{0.9}\\ a_5=20000\end{array}$

Therefore, total amount Job B will pay is $\$20000$ .