Question 13 of 14>If you deposit P dollars in a retirement fund every year for N years with the intention of then withdrawing Q dollars per yearfor M years, you must earn interest at a rater satisfyingP (bN - 1)(1-b-M)where b 1 + rAssume that $2100 is deposited each year for 27 years and the goal is to withdraw $7500 per year for 10 yearsUse Newton's Method to compute r.(Use decimal notation. Give your answer to two decimal places.)r =96

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Asked Nov 15, 2019
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Question 13 of 14
>
If you deposit P dollars in a retirement fund every year for N years with the intention of then withdrawing Q dollars per year
for M years, you must earn interest at a rater satisfying
P (bN - 1)
(1-b-M)
where b 1 + r
Assume that $2100 is deposited each year for 27 years and the goal is to withdraw $7500 per year for 10 years
Use Newton's Method to compute r.
(Use decimal notation. Give your answer to two decimal places.)
r =
96
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Question 13 of 14 > If you deposit P dollars in a retirement fund every year for N years with the intention of then withdrawing Q dollars per year for M years, you must earn interest at a rater satisfying P (bN - 1) (1-b-M) where b 1 + r Assume that $2100 is deposited each year for 27 years and the goal is to withdraw $7500 per year for 10 years Use Newton's Method to compute r. (Use decimal notation. Give your answer to two decimal places.) r = 96

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Expert Answer

Step 1
Given that P $2100,N 27, Q=$7500 and M 10. Substitute these values
in the given equation as follows.
P(b'-1)-(1-b where b =1+r
2100(67-1) 7500 (1-b10)
1
21b2-21 75-75
21h27+10 21b10 = 75b10 -75
21b37 -96b10
75 0
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Given that P $2100,N 27, Q=$7500 and M 10. Substitute these values in the given equation as follows. P(b'-1)-(1-b where b =1+r 2100(67-1) 7500 (1-b10) 1 21b2-21 75-75 21h27+10 21b10 = 75b10 -75 21b37 -96b10 75 0

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Step 2
consider the function f(x)=21x37 -96x10 +75
In order to compute the positive root of the above equation, start with x =1
in newton's method
Let the function be f(x) 21r
-96x0 +75 and x, =1
www.
f(x) 21r37-96x10 + 75
Calculate
the
derivative
of
as
www
f'(x)=777x36 -960x*
f (x)
=x,
Note that, the Newton Raphson method is given by x,
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consider the function f(x)=21x37 -96x10 +75 In order to compute the positive root of the above equation, start with x =1 in newton's method Let the function be f(x) 21r -96x0 +75 and x, =1 www. f(x) 21r37-96x10 + 75 Calculate the derivative of as www f'(x)=777x36 -960x* f (x) =x, Note that, the Newton Raphson method is given by x,

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Step 3
Now, compute the value of x using Newton Raphson method as follows
f(x)
21(1)-96(1)+75
777(1)6-960 (1)
=1-
=1
-183
Now, since its gives the same value 1, Start with x, =1.1
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Now, compute the value of x using Newton Raphson method as follows f(x) 21(1)-96(1)+75 777(1)6-960 (1) =1- =1 -183 Now, since its gives the same value 1, Start with x, =1.1

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