Refer to Problem 39 . John procrastinates and does not make his first $1,000 deposit into an IRA until he is 36 . But then he continues to deposit $1,000 each year until he is 65 ( 30 deposits in all). If John's IRA also earns 6.4 % compounded annually, how much is in his IRA when he makes his last deposit on his 65 th birthday?
Refer to Problem 39 . John procrastinates and does not make his first $1,000 deposit into an IRA until he is 36 . But then he continues to deposit $1,000 each year until he is 65 ( 30 deposits in all). If John's IRA also earns 6.4 % compounded annually, how much is in his IRA when he makes his last deposit on his 65 th birthday?
Solution Summary: The author calculates the amount earned in the IRA when John makes his last deposit on his 65th birthday.
Refer to Problem
39
. John procrastinates and does not make his first
$1,000
deposit into an IRA until he is
36
. But then he continues to deposit
$1,000
each year until he is
65
(
30
deposits in all). If John's IRA also earns
6.4
%
compounded annually, how much is in his IRA when he makes his last deposit on his
65
th
birthday?
Give an example of a graph with at least 3 vertices that has exactly 2 automorphisms(one of which is necessarily the identity automorphism). Prove that your example iscorrect.
3. [10 marks]
Let Go (Vo, Eo) and G₁
=
(V1, E1) be two graphs that
⚫ have at least 2 vertices each,
⚫are disjoint (i.e., Von V₁ = 0),
⚫ and are both Eulerian.
Consider connecting Go and G₁ by adding a set of new edges F, where each new edge
has one end in Vo and the other end in V₁.
(a) Is it possible to add a set of edges F of the form (x, y) with x € Vo and y = V₁ so
that the resulting graph (VUV₁, Eo UE₁ UF) is Eulerian?
(b) If so, what is the size of the smallest possible F?
Prove that your answers are correct.
Let T be a tree. Prove that if T has a vertex of degree k, then T has at least k leaves.
Chapter 3 Solutions
Finite Mathematics for Business, Economics, Life Sciences and Social Sciences
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