Special Assignment Three is a GROUP PROJECT. All papers must be
worked on and written up by groups of at least two and no more
than four people. TYPE the group writeup. Please use complete
sentences to explain your work and answers. For graphs, you may
attach neat free hand sketches with enough labels for an outsider
to understand the graph. Groups may assign tasks, but each member
is responsible for understanding all parts of the assignment. The
last paragraph should summarize the roles and activity of each
group member.
•
Please note: Using the results of another group without
acknowledgment is considered academic dishonesty and will be
severely punished.
•
Turn in the Antipasto, Main
Course, and Dessert.
Present Value and Future Value of a Continuous Income/Investment Stream
See Hoffmann, pp. 422-425.
For SA3 we shall assume an "investment" or "account" earns at an
annual rate of r = 3.7% CC (compounded continuously).
Antipasto - Turn In!
A1. Money is deposited continuously in an account at a rate of
$1000 per year, what is the value of the account after T = 15
years?
Typing suggestion: Borrowing from Maple or your calculator, you
may type ∫ab f(t) dt as
int(f(t), t = a .. b).
or
fnInt(f(t),t,a,b).
A2. Money is deposited continuously in an account at a rate of
$1000 per year for a period of T years. At the end of T
years the value of the account is $10000. What is the value of
T?
Your solution should include a sentence of the form: Solve
the equation … = … for T ….
A3. I have just enough money in an account so that money may be withdrawn continuously at a rate of
$1000 per year for T = 15 years. What is the present value of
the account?
A4. My account starts with $10000, and money is
withdrawn at a rate of $1000 per year for T years. What is
the value of T? (When does the account have 0 balance?)
Main CoursePlease use complete sentences to explain your work and
answers.
M1. Beginning at age 65, I wish to withdraw $12000 per year for 20
years. What should be the value of the account when I am 65? Call
this number A65 - the assets needed at age 65 to "buy"
the annuity.
M2. If I start contributing (continuously of course) to the account at age 55,
at what annual rate must I contribute to have the value
A65 at age 65?
M3. If I start contributing (continuously of course) to the account at age 45,
at what annual rate must I contribute to have the value
A65 at age 65?
M4. I can contribute only at the rate of $6000 per
year. At what age do I need to start contributing to have the
value A65 at age 65?
M5. I can contribute only at the rate of $3000 per
year. At what age do I need to start contributing to have the
value A65 at age 65?
Dessert: Annuities with COLA (Cost of Living
Adjustment)
Assume that inflation is occurring at 2% per year CC.
COLA1. Beginning at age 65, I wish to withdraw from an account for 20 years. I will begin
the withdrawals at the rate of $12000 per year. The payments
will have a COLA (cost of living adjustment) so that at age 65 +t years I will be withdrawing at a rate of $12000*e.02 t
per year. What should be the value of the account when I am 65?
Call this number ACOLA65 - the assets needed at age 65
to "buy" the annuity with the COLA.
COLA2.
At age 45, I start contributing (continuously of course) to the account. My initial rate
is $R45 per year, which I continually adjust for
inflation so that at age 45 + t years I will be contributing at
rate of $R45*e.02 t per year. At what initial annual
rate $R45 must I contribute to have the value
ACOLA65 at age 65?
Remember the Rules
The last paragraph of your typed writeup should summarize the
roles and activity of each group member.
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TTH,
version 4.04. On 22 Aug 2014, 20:56.