Explanation Formula used: Sum of first n terms: 1. The sum of first n terms in arithmetic sequences is S n = n 2 ( 2 a 1 + ( n − 1 ) d ) , where a 1 is first term and d is common difference. 2. The sum of first n terms in geometric sequences is S n = a ( 1 − r n 1 − r ) , where a 1 is first term and r is common ratio. Calculation: It is given that the 5 year contract with a first year salary is $ 1 , 500 , 000 . The client has three choices. Option A is a bonus of $75,000 each year including first year. The total money of the five-year period in option A is obtained as follows. The total amount per year is 1 , 500 , 000 + 75 , 000 = 1 , 575 , 000 . Total amount is 5 ( 1 , 575 , 000 ) = 7 , 875 , 000 . Thus, the total amount in option A is $ 7 , 875 , 000 . The total amount of 5-year period in option B is obtained as follows: Option B is the annual increase is 4% per year beginning after the first year. This forms a geometric sequence and the first term is $1,500,000, the second term is 1 , 500 , 000 + 4 % ( 1 , 500 , 000 ) = 1 , 500 , 000 ( 1 + 0.04 ) and so on Thus, the common ratio is 1 + 0.04 = 1.04 . In order to find the total amount of period 5 year, find the value of S 5 . Substitute a = 1 , 500 , 000 , r = 1.04 , and n = 5 in S n = a ( 1 − r n 1 − r ) . S 5 = 1 , 500 , 000 ( 1 − ( 1.04 ) 5 1 − 1.04 ) = 1 , 500 , 000 ( 1 − 1 .21665 − 0 .04 ) = 1 , 500 , 000 ( − 0

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ISBN: 9780321880116

Author: Michael Sullivan III, Katherine R. Struve, Janet Mazzarella

Publisher: PEARSON

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Chapter 13.3, Problem 84E

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The option that provides the most money over the 5-year period and least money over the 5-year.

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Chapter 13.3, Problem 83E

Chapter 13.3, Problem 85E

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Chapter 13 Solutions

Elementary & Intermediate Algebra

Ch. 13.1 - A(n) _____ is a function whose domain is the set...Ch. 13.1 - Prob. 2E Ch. 13.1 - Prob. 3E Ch. 13.1 - Prob. 4E Ch. 13.1 - Prob. 5E Ch. 13.1 - Prob. 6E Ch. 13.1 - Prob. 7E Ch. 13.1 - Prob. 8E Ch. 13.1 - Prob. 9E Ch. 13.1 - Prob. 10E

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The option that provides the most money over the 5-year period and least money over the 5-year.

Solution Summary: The author explains that the option that provides the most money over the 5-year period is underset_OptionC, while the less money option provides more money.

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The option that provides the most money over the 5-year period and least money over the 5-year.

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Chapter 13 Solutions