Group Project
Lottery Annuities

The Project

There are numerous games in the Connecticut lottery, each of which would be considered a scam if run by a private business. They all do pay out prize money, but the vast majority of bettors wind up losing.

Winners of large prizes are given the option of being paid their winnings as a lump sum or in the form of an annuity. The lump sum is considerably less than the advertised winnings; the annuity consists of payments made annually until the advertised amount won is distributed.

Consider a nominal prize of one million dollars, to be paid in twenty annual payments of $50,000. Assume when each payment is made, the recipient immediately pays Federal income tax at a 25% rate, Connecticut state income tax at a 5% rate and invests the rest.

Assume the funds invested earn 6% per year, with both Federal and Connecticut state income taxes paid from that income and the remainder reinvested.

The Assignment

  1. Determine the total amount of money the winner will have at the end of twenty years. This will be one year after the last payment.
  2. Determine the amount the winner would have had at the end of twenty years if he or she had been given one million dollars all at once under the same conditions regarding taxes and investment.
  3. Determine the amount for a lump sum payment that would leave the winner with the same amount as the annuity after twenty years.
  4. Analyze the pros and cons of lump sum payments vs. annuities.
  5. Discuss assumptions that were made to simplify this assignment along with important factors that have been omitted.

The Ground Rules

This project will be completed by competing groups/teams. The teams are listed below.

Some time will be given in class for the teams to get organized, but the bulk of the work is to be done outside of class.

The project will be graded on the basis of 100 points, but will be given a weight of ½ for the purposes of calculating averages. In other words, it will be worth half as much as an exam.

Except in exceptional purposes, each group member will receive the same grade. One of the main purposes of the team performance agreement is to ensure that each person pulls his or her weight and earns his or her grade.


The project report should be self-contained. Any formulas used, other than a simple calculation of interest, needs to be derived.

Each group will create a written report, which may include charts and sketches if deemed appropriate. The report must include the names of all team members.

An electronic copy of the text must also be submitted to the instructor by electronic mail. The electronic copy should be in plain text (ascii). It should be in the body of the email message, not an attachment. Optionally, groups may submit their projects electronically as html, but that should still be in plain text. The only exception is that if any graphics are included, they may (indeed, must) be sent as attachments. Note it is likely that some information in the written report will be lost.

Alternative: In place of submitting the electronic copy directly, students may create a web page and communicate the url for the web page.

The reports should be prepared so that they would be understood by students with backgrounds similar to those of the students in the class. No prior knowledge of the project should be necessary to fully understand what the assignment was. The report should not contain a reproduction of this sheet; the report must be understandable simply because it is clearly written.

Reports should be mostly self-contained in that they generally should not require the reader to check outside sources, or to trust outside sources, to verify any information. If any formulas are used, they should be explained and, if not generally known by the typical college student, derived. For example, one would not need to derive the formula for the area of a circle but one would need to derive the formula for the present value of an annuity.

Use may be made of standard software, such as spreadsheets. In such cases, their use must be completely explained.

Students who are able to program in standard languages may do so with the permission of the instructor.

Research may be done using Internet, but no use may be made of sites which do calculations for users.

It is recommended that each team member carefully analyze the completed report prior to its submission from the perspective of someone who has no knowledge of the project to make sure that it is written clearly enough, with sufficient explanation so that, for example, someone reading the report would be able to reproduce exactly the same calculations included without looking at those calculations.

All reports will be posted on the course home page.

Confidential Individual Reports

In addition to the team's report, each team member will, in confidence, separately submit an individual report describing how the team divided up the tasks and including an estimate of the percentage contribution of each team member.

Students who do not submit their individual confidential reports by the due date will be penalized. Also, if there is a general consensus within a group that some team members did not contribute their fair share, those students will be penalized.


Each group will prepare a contract, called a team performance agreement, due Monday, September 22. The contract will be graded and will count for 20% of the project grade.

The final report for each group is due Monday, October 6. Groups are encouraged to submit their final reports before the due date; no reports will be accepted after the due date.

Sample Report

View a Sample Report

The Groups

Click on the group to view its report.

8:00 Class

Group 1
Lindsay Bissonnette, James Gerosa, Alyssa Huddleston, Jennifer Rosa, Amy Tran

Group 2
Anthony Calandro, Chris Cardenas, Kevin Daigle, Sara Dobensky, Matthew Stone, Justin Toro

Group 3
Chase Chemero, Daniel Hanley, Sonja Henst, Luis Macancela, Maxim Shorey, Thanh Tran

Group 4
Agne Bileviciute, Karen Carlson, Robert Deschino, Daniel Marcil, Brandon Sweet

Group 5
Chad Boulier, Joseph Ciarleglio, Michelle Gravel, Sara Lima, Cristina Nocito

9:30 Class

Group 1
Jeffrey Albert, Nicole Borges, Zachary Byler, Julian Chan, Eric Chhom, Joshua Sanford

Group 2
Timothy Cawley, Daniel Curtis, Igli Cyreku, Luis Enriquez, Fernando Piedra, Jonathan Trudeau

Group 3
Michael Bogush, Frank Caruso, Timothy Gaipa, Blayze Markoya, Steven Panzella, Shawn Smith

Group 4
Manal Ahmad, Leo Carey, Eric Demmons, Ryan McNally, David Sanchez, Eric Trimborn

Group 5
Tyler Larrivee, Stephen Miske, Pedro Muniz, Habibullah Olomi, Theodore Petrahai