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?
Q2: Using the Laplace transform, find the solution for the following equation
y"" +y" = 6et + 6t + 6. Suppose zero initial conditions (y"" (0) = y"(0) = y'(0) = y(0) = 0).
1- Let A = {A1, A2, ...), in which A, A, = 0, when i j.
a) Is A a π-system? If not, which element(s) should be added to A to become a π-system?
b) Prove that σ(A) consists of the finite or countable unions of elements of A; i.c., A E σ(A) if and
only if there exists finite or countable sequence {n} such that A = U₁An (Hint: Let F be such
class; prove that F is a σ-filed containing A.)
c) Let p ≥ 0 be a sequence of non-negative real numbers with Σip₁ = 1. Using p₁'s, how do you
construct a probability measure on σ(A)? (Hint: use extension theorem.)
2- Construct an example for which P(lim sup A,) = 1 and P(lim inf An) = 0.
3. Let
f(z) =
sin (22) + cos (T2)
2(22+1)(z+1)
Compute f(z)dz over each of the contours/closed curves C1, C2, C3 and C4 shown
below.
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Chapter 3 Solutions
Finite Mathematics for Business, Economics, Life Sciences and Social Sciences
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