## 9:320 AM Class Group 2

Group 2 9:30 class math 1070 Math project electronic copy Lottery Winnings Finding the Truth Report October 6, 2008 Group 2: Luis Enriquez Fernando Piedra Timothy Cawely Jonathan Trudeau Igli Cyreku Daniel Curtis This Report contains the investigations and findings of Group 2 in effort to explain and bring to light certain hidden parts of ct lottery winnings. The task is to figure out five alternatives and questions of a one million dollar winnings of a lottery. The guidelines for the winnings deal with the whole sum being paid out in 20 years. $50,000 each year minus a total of 30% in annual taxes split into a 25% federal tax and a 5% ct income tax. The next portion of the task assumes that the winner will invest his or her winnings and has an annual return of 6% which then in turn additionally gets taxed again another 30% split in the same way as in the original winnings payment each year. The assignment is as follows: 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. 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. The final outcome for the total winnings to the 1st part of the assignment after the 20 year period is $519,400. In the first assignment, simple mathematics took place. Calculations went as the following. A series of payments were done as shown below: 1. 25970 2. 51940 3. 77910 4. 103880 5. 129850 6. 155820 7. 181790 8. 207760 9. 233730 10. 259700 11. 285670 12. 311640 13. 337610 14. 363580 15. 389550 16. 415520 17. 441490 18. 467460 19. 493430 20. 519400 The calculations went as the following: 1st payment: (50000*0.3)-50000=35000*.06=37100*.3= 25970 37100-[(35000+2100)*.3] + 25970 to give us the rest of the payments in sequence after the first payment. Additionally the annuity is calculated and then displayed via the same mathematical process in the chart below under the annuity portion. Annuity* vs. Lump Sum* 36470 729400 74471.74 760034.8 114063.6 791956.3 155330.5 825218.4 198319.4 859877.6 243118.8 895992.5 289799.8 933624.2 338441.3 972836.4 389125.9 1013696 441939.2 1056270 496970.6 1100694 554313.4 1146860 614064.5 1195028 676325.3 1245220 741200.9 1297519 808801.3 1352015 879241 1408799 952639.1 1467969 1029119 1529624 1108813 1593868 *note: the payments descend from top which is 1st payment down to last. 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. Here the same method as set one was taken except that this time instead of payments made annually only the taxes were taken out from each year. The one big some of money given all at once is simply just given to the winner then taxes are taken out each year and a 6% growth of investment is given back. The calculations are displayed below under the lump sum portion of the comparison. Refer to the list of numbers below: Annuity* vs. Lump Sum* 36470 729400 74471.74 760034.8 114063.6 791956.3 155330.5 825218.4 198319.4 859877.6 243118.8 895992.5 289799.8 933624.2 338441.3 972836.4 389125.9 1013696 441939.2 1056270 496970.6 1100694 554313.4 1146860 614064.5 1195028 676325.3 1245220 741200.9 1297519 808801.3 1352015 879241 1408799 952639.1 1467969 1029119 1529624 1108813 1593868 *note: the payments descend from top which is 1st payment down to last. The chart shows the one lump sum method being the best method as the winner will get more money and the winner will in the end receive more winnings than in regular annuity or with regular payments. Determine the amount for a lump sum payment that would leave the winner with the same amount as the annuity after twenty years. This section uses the scenario of the winner being given one lump sum instead of annual payments but however still leave the winner with the same amount as with the resulting amount of part 2 of the assignment. In this we used a nice and easy method along with excel to reach this formula : [P-(1-i)] +R]-(1-i)] + S P=payment I= Taxes R=investment return % S= net amount of money received from previous year 1. 52998.6 2. 105997.2 3. 158995.8 4. 211994.4 5. 264993 6. 317991.6 7. 370990.2 8. 423988.8 9. 476987.4 10. 529986 11. 582984.6 12. 635983.2 13. 688981.8 14. 741980.4 15. 794979 16. 847977.6 17. 900976.2 18. 953974.8 19. 1006973 20. 1059972 In this method we see a slight variation between the amounts in parts 1 and 2 but this was the initial trial. By then using the guess and check method along with the other knowledge from previous calculations we figured out the lump sum amount needed was 712,000 to equal the same amount as the annuities as placed by the original calculation 1,108,813. We narrowed down a figure as each calculation went by until we reached the target number of 712,000 for being the lump sum amount needed in the beginning to end up with 1,108,813 in accordance to our formula. Analyze the pros and cons of lump sum payments vs. annuities Annuity Pros Cons You have another source of income for 20 years. You don’t know how much 1.2 mil will be worth in 20 years. You don’t have as much money as you would with the lump sum. Lump Sum Pros Cons You have about 200,000 more than with If you get the money all at one time it is easier annual payments to ‘blow’ or spend the money quicker In much respect we can tell that the best way is to receive the lump sum payments rather than payments since payments will only result in less money however that is the game and way most lotteries operate so it is hard to get what you really win. In any case, it is safe to assume that if ever given the choice lump sum method would be the best to go in any prize winnings rather than annual payments. Discuss assumptions that were made to simplify this assignment along with important factors that have been omitted. Assumptions That Were Made and Other Important Factors That Have Been Omitted The federal tax rate The Connecticut tax rate A stable, never changing market Never changing federal or local tax rates The lottery commission will continue to pay an annuity You actually won the lottery No interest used calculated The lottery is won in Connecticut The person who wins responsibly spends