Listed below are the various projects that will be required throughout the semester. Each of these
are worth 25 points and will be due the day following the exam for the appropriate chapter.
These projects take you above and beyond the material covered in the book or require outside
data acquisition. You may work in groups of up to three people per project. Turn in one project
with all group member's names on it. Plan on reading the section of the book dealing with the
matter before we cover it in class; you will not always have time to finish the project if you wait
until we do. Give me the results of any surveys along with the projects.
Project 1, Chapter 4
Your project is to plan a retirement fund for yourself. To simplify calculations, assume all
transactions - starting of annuity fund, retirement, and death - occur on your birthday. Assume a
nominal interest rate of 6% has been guaranteed for the remainder of your life.
- Identify the age you will be on your birthday this year.
- Identify the age at which you wish to retire. Identify the number of years before
- Identify the age at which you anticipate dying. Identify the number of years of retirement.
- Identify the monthly payment you anticipate needing during your retirement.
- Calculate the present value necessary on the date of retirement to finance your retirement.
- The present value needed to retire is the future value necessary upon retirement. Calculate
the monthly payment needed before retirement to have enough money to retire.
- Calculate the amount of money in your retirement fund after ten years assuming you make
the regular payments just calculated.
- After the ten years, assume that you receive an inheritance of $50,000 and add it to your
retirement fund. If you stop making regular payments, and just let what money is in the
account draw interest, what will the amount be at the time of retirement?
- Subtract this amount from the future value needed upon retirement and recompute the
monthly payment necessary to obtain the future value. Remember that ten years have
Project 2, Chapter 5
Amtrak® has several lines running in Illinois with Bus links between other cities. Consider the
cities: Bloomington, Carbondale, Chicago, Galesburg, Joliet, St. Louis, and Urbana. The train or
bus stops at each town along the route, but for purposes of this project, only consider the towns
listed above. See Amtrak's route information on the world wide web http://www.dot.state.il.us/
- Create an incidence matrix for the routes between the cities.
- How many ways can a passenger get from Joliet to Bloomington with no stops in-between
(again, only consider the seven cities listed)?
- How many ways can a passenger get from Joliet to Bloomington with exactly one stop
between? With either 0 or 1 stop between?
- How many ways can a passenger get from Joliet to Bloomington with exactly two stops
between? With either 0, 1, or 2 stops between?
- How many ways can a passenger get from Joliet to Bloomington with exactly three stops
between? With either 0, 1, 2, or 3 stops between?
Project 3, Chapter 7
For each of the winning poker hands listed below, give the number of ways that hand can be
obtained and the probability of obtaining that hand.
- Royal Flush - (Five highest cards from ten through ace in any single suit)
- Straight Flush - (Five cards of the same suit in numerical order)
- Four of a Kind
- Full House - (Three of one kind of card and two of another)
- Flush - (Five cards of the same suit)
- Straight - (Five cards in sequence but not the same suit)
- Three of a Kind
- Two Pairs
- One Pair
Project 4, Chapter 8+
Consider this gambler's ruin problem: Two people have a total of five $1 bills June between them.
A fair coin is tossed. If a head appears, then player A gets $1; if a tail appears, then player B gets
$1. The game continues until one player has all the money and the other player is ruined (hence
This game can be analyzed using absorbing Markov Chains.
- Draw a transition diagram.
- Write the transition matrix
- Find the fundamental matrix and limiting matrix.
- What is the probability that player A will win all of the money if (s)he starts with $1, $2,
$3, or $4?
- What is the average number of coin tosses until the game ends if player A starts with $1,
$2, $3, or $4?
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