a) Explanation Given Information: The first term is $ 1000 and compound interest is 4 % and in each term of geometric sequence is representing the amount in the account at the beginning of each year. Formula used: (1) The amount of the compound interest is given by, A = P ( 1 + R 100 ) n Where, A = Amount, P = Principle, R = Rate of interest and n = number of years (2) The n t h term of geometric sequence, a n = a 1 r n − 1 Where, a 1 is the first term, n is the number of terms and r is the factor between the terms (common ratio). Calculation: Consider the first term is $ 1000 and compound interest is 4 % and in each term of geometric sequence is representing the amount in the account at the beginning of each year. The amount of the compound interest is given by, A = P ( 1 + R 100 ) n …… (1) Where, A = Amount, P = Principle, R = Rate of interest and n = number of years Put the value of P = $ 1000 , R = 4 % and n = 1 in equation (1) A = P ( 1 + R 100 ) n = $ 1000 ( 1 + 4 100 ) 1 = $ 1000 ( 1 + 1 25 ) = $ 1000 ( 26 25 ) 1 Thus, A = $ 1000 ( 26 25 ) 1 The general term of the geometric sequence is a 1 , a 1 r , a 1 r 2 , a 1 r 3 , … And n t h term, a n = a 1 r n − 1 Where a 1 is the first term, n is the number of terms and r is the factor between the terms (common ratio) b) To determine To calculate: The general term of the sequence in which $ 1000 is invest at 4 % compound interest includes interest paid on interest that was previously earned. c) To determine To calculate: How much money will collect after 20 years in which given $ 1000 is invest at 4 % compound interest at the beginning of next year.

Pearson eText Elementary and Intermediate Algebra: Concepts and Applications -- Instant Access (Pearson+)

7th Edition

ISBN: 9780137361847

Author: Marvin Bittinger, David Ellenbogen

Publisher: PEARSON+

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Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence. It was invented by German mathematician Carl Friedrich Gauss.

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Chapter 14, Problem 2DMC

To determine

To calculate: The geometric sequence with each term representing the amount in the account at the beginning of each year. in which first term is $1000 and compound interest is 4%.

To determine

To calculate: The general term of the sequence in which $1000 is invest at 4% compound interest includes interest paid on interest that was previously earned.

To determine

To calculate: How much money will collect after 20 years in which given $1000 is invest at 4% compound interest at the beginning of next year.

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Chapter 14, Problem 1DMC

Chapter 14, Problem 3DMC

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Chapter 14 Solutions

Pearson eText Elementary and Intermediate Algebra: Concepts and Applications -- Instant Access (Pearson+)

Ch. 14.1 - Prob. 1YT Ch. 14.1 - Prob. 2YT Ch. 14.1 - Prob. 3YT Ch. 14.1 - Prob. 4YT Ch. 14.1 - Prob. 5YT Ch. 14.1 - Prob. 1CYU Ch. 14.1 - Prob. 2CYU Ch. 14.1 - Prob. 3CYU Ch. 14.1 - Prob. 4CYU Ch. 14.1 - Prob. 5CYU

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The geometric sequence with each term representing the amount in the account at the beginning of each year. in which first term is $ 1000 and compound interest is 4 % .

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To calculate: The geometric sequence with each term representing the amount in the account at the beginning of each year. in which first term is $1000 and compound interest is 4%.

To calculate: The general term of the sequence in which $1000 is invest at 4% compound interest includes interest paid on interest that was previously earned.

To calculate: How much money will collect after 20 years in which given $1000 is invest at 4% compound interest at the beginning of next year.

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Chapter 14 Solutions