Explanation Formula used: Geometric sequences: 1. The n th terms of the sequence is a n = a 1 r n − 1 , where a 1 is first term and r is common ratio. 2. The sum of first n terms in 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 a person is interviewing for a job and received two offers. Option A is start $30,000 with guaranteed annual increases of 5% for the first 5 years. The first year is a 1 = 30 , 000 . The amount in second year is computed as follows. a 2 = 30 , 000 + 5 % of 30 , 000 = 30 , 000 + 0.05 ⋅ 30 , 000 = 30 , 000 ( 1.05 ) The amount in third year is computed as follows. a 3 = a 2 + 5 % of a 2 = a 2 ( 1.05 ) Every year of salary makes a geometric sequence. The sequence is 30,000, 30 , 000 ( 1.05 ) , 30 , 000 ( 1.05 ) ( 1.05 ) ,…. In order to find the 5 th year of money, find the 5 th term of the sequence. Substitute a 1 = 30 , 000 , r = 1.05 , and n = 5 in a n = a 1 r n − 1 . a 5 = ( 30 , 000 ) ( 1.05 ) 5 − 1 = ( 30 , 000 ) ( 1.05 ) 4 = 30000 ⋅ 1.21550625 ≈ 36465 .19 Therefore, the money in 5 th year for option A is $36465 .19 . The total amount of 5-year period in option A is obtained as follows: Substitute a 1 = 30 , 000 , r = 1.05 , and n = 5 in S n = a ( 1 − r n 1 − r ) . S 5 = ( 30 , 000 ) ( 1 − ( 1.05 ) 5 1 − 1.05 ) = ( 30 , 000 ) ( 1 − ( 1.05 ) 5 1 − 1.05 ) = ( 30 , 000 ) − 0 .2762815625 − 0 .05 = 8288.44688 0 .05 = 165,768

3rd Edition

ISBN: 9780321880116

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

Publisher: PEARSON

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Chapter 13.3, Problem 83E

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The best offer that makes more money as possible after the 5^th year and find the best offer to make more money as possible over entire 5 years.

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Chapter 13.3, Problem 82E

Chapter 13.3, Problem 84E

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The best offer that makes more money as possible after the 5 th year and find the best offer to make more money as possible over entire 5 years.

Solution Summary: The author explains how to find the best offer that makes more money after the 5th year and the larger annual salary over the five years.

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The best offer that makes more money as possible after the 5^th year and find the best offer to make more money as possible over entire 5 years.

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The best offer that makes more money as possible after the 5 th year and find the best offer to make more money as possible over entire 5 years.

Solution Summary: The author explains how to find the best offer that makes more money after the 5th year and the larger annual salary over the five years.

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The best offer that makes more money as possible after the 5th year and find the best offer to make more money as possible over entire 5 years.

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Chapter 13 Solutions

The best offer that makes more money as possible after the 5^th year and find the best offer to make more money as possible over entire 5 years.