Explanation Given: The value of portfolio of bonds P ( r ) depends on the interest rate r . The value of the function P ( r ) at r = 5 is, P ( 5 ) = 100 , 000 The first differentiation of the function P ( r ) at r = 5 is, d P d r = − 40 , 000 The second differentiation of the function P ( r ) at r = 5 is, d 2 P d r 2 = 50 , 000 Concept used: The n th Taylor polynomial centered at x = a can be expressed as, T n ( x ) = f ( a ) + f ′ ( a ) 1 ! ( x − a ) + f ″ ( a ) 2 ! ( x − a ) 2 + ⋯ + f n ( x ) n ! ( x − a ) n …… (1) The second Taylor polynomial can be written as, T 2 ( x ) = f ( a ) + f ′ ( a ) 1 ! ( x − a ) + f ″ ( 0 ) 2 ! ( x − a ) 2 …… (2) Calculation: To obtain the second Taylor polynomial of function P ( r ) , replace x by r and f by P in the equation (2) as, T 2 ( r ) = P ( a ) + P ′ ( a ) 1 ! ( r − a ) + P ″ ( a ) 2 ! ( r − a ) 2 …… (3) Substitute 5 for a in the equation (3) to obtain the second Taylor polynomial of function P ( r )

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 9.4, Problem 56E

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To find: The second Taylor polynomial of P(r) centered at r=5 and the value of portfolio for interest rate r=5.5% .

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Chapter 9.4, Problem 55E

Chapter 9.4, Problem 57E

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Chapter 9 Solutions

Calculus - Standalone book

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The second Taylor polynomial of P ( r ) centered at r = 5 and the value of portfolio for interest rate r = 5.5 % .

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Chapter 9 Solutions