College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter 8 - Sequences, Induction, and Probability - Exercise Set 8.3 - Page 741: 74

Answer

Total salary over 5 years by company A = 169112.8 Total salary over 5 years by company B = 169892.3 Company B offers better total salary for a five year contract. Company B offers = 779.5 more than company A.

Work Step by Step

Company A offers salary on first year $a_{1}$ = 30000 As company A increase salary 6% each year means the salary multiply by 1.06 each year, so common ratio = 1.06 Total salary calculated for 5 years then n = 5 Total salary over n years is given by sum formula $S_{n}$ = $a_{1}$$\frac{(1 - r^{n})}{(1 - r)}$ Total salary over 5 years by company A $S_{5}$ = 30000$\frac{(1 - 1.06^{5})}{(1 - 1.06)}$ = 30000$\frac{(1 - 1.338)}{(1 - 1.06)}$ = 30000$\frac{(-0.338)}{(-.06)}$ = 30000$\times$5.64 = 169112.8 Company B offers salary on first year $a_{1}$ = 32000 As company B increase salary 3% each year means the salary multiply by 1.03 each year, so common ratio = 1.03 Total salary calculated for 5 years then n = 5 Total salary over n years is given by sum formula $S_{n}$ = $a_{1}$$\frac{(1 - r^{n})}{(1 - r)}$ Total salary over 5 years by company B $S_{5}$ = 32000$\frac{(1 - 1.03^{5})}{(1 - 1.03)}$ = 32000$\frac{(1 - 1.159)}{(1 - 1.03)}$ = 32000$\frac{(-0.159)}{(-.03)}$ = 32000$\times$5.31 = 169892.3 Total salary over 5 years by company A = 169112.8 Total salary over 5 years by company B = 169892.3 Company B offers better total salary for a five year contract. Company B offers 169892.3 - 169112.8 = 779.5 more than company A.
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