# Finite Projects

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 retirement.
• 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 gone by.

### 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 the name).

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?

Last updated: Sunday, June 9, 1996 at 9:35 pm