Explanation Given information: The investment is $ 500 and the returns for the first, second, and third months are $ 100 , $ 200 , and $ 300 respectively. Explanation: Let’s assume the internal rate per month is i If $ 500 is invested for three months, then the final amount after three months would be A = 500 ( 1 + i ) 3 . But, $ 100 returned at the end of the first month, so there wasn’t any interest on $ 100 for the next two months. That is, A 1 = 100 ( 1 + i ) 2 Similarly, $ 200 returned at the end of second month, so there wasn’t any interest on $ 200 for one month. That is, A 2 = 200 ( 1 + i ) Finally, $ 300 returned at the end of third month. By combing all the above investments and returns, then the equation becomes A − A 1 − A 2 − 300 = 0 . By substituting values of A , A 1 , and A 2 ⇒ 500 ( 1 + i ) 3 − 100 ( 1 + i ) 2 − 200 ( 1 + i ) − 300 = 0 By substituting ( 1 + i ) = x ⇒ 500 x 3 − 100 x 2 − 200 x − 300 = 0 ⇒ f ( x ) = 500 x 3 − 100 x 2 − 200 x − 300 Now, roughly graph the function by using the curve-sketching techniques to get the value of x 0 By applying the curve-sketching techniques, a rough sketch of the graph of f ( x ) = 500 x 3 − 100 x 2 − 200 x − 300 is as below. From the graph, it is observed that x − intercept lies in between 1 and 2 , so x 0 = 1 The formula for the Newton-Raphson algorithm is x new = x old − f ( x old ) f ' ( x old ) So, differentiate f ( x ) with respect to x ⇒ f ' ( x ) = 1500 x 2 − 200 x − 200 Substitute the value of x 0 in f ( x ) and f ' ( x ) , and calculate f ( x 0 ) and f ' ( x 0 ) respectively

Pearson eText for Calculus & Its Applications -- Instant Access (Pearson+)

14th Edition

ISBN: 9780137400096

Author: Larry Goldstein, David Lay

Publisher: PEARSON+

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Chapter 11.2, Problem 13E

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The internal rate of return of an investment, when $ 500 yields returns of $ 100, $ 200, and $ 300 at the end of first, second, and the third months respectively.

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Chapter 11.2, Problem 12E

Chapter 11.2, Problem 14E

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The internal rate of return of an investment, when $ 500 yields returns of $ 100 , $ 200 , and $ 300 at the end of first, second, and the third months respectively.

Solution Summary: The author explains that the internal rate of return of an investment is 8.21% per month.

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The internal rate of return of an investment, when $ 500 yields returns of $ 100, $ 200, and $ 300 at the end of first, second, and the third months respectively.

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Chapter 11 Solutions