## 8 AM Class Group 5

Chad Boulier Joseph Ciarleglio Michelle Gravel Cristina Nocito Sara Lima Math 1070Q Group Project Lottery Annuities The project entailed determining the resolution to several different situations regarding the winnings received from the Connecticut lottery. The recipient of the Connecticut lottery had the option of receiving the winnings of $1,000,000.00 either as one lump sum or twenty annual payments of $50,000.00. Under the presumption that the recipient paid Federal income tax of 25% and Connecticut income tax of 5% upon receiving each annual payment and investing the remaining earnings, the invested remainder will earn 6% interest per year. 1.) To determine the annuity portion of the project, or the projected balance after investing the remaining funds and collecting interest for twenty years, our group decided that our first step would be to deduct the Federal tax income of 25% as well as the Connecticut tax income of 5% from each payment of $50,000.00. To simplify computing the problem, we combined 25% and 5% which gave us 30% as our new sum to deduct from the payment of $50,000.00. To compute the percentage, we multiplied $50,000 by .3 giving us $15,000. The $15,000 would then be subtracted from $50,000 giving us $35,000 which would be the funds remaining to be invested after taxes have been deducted. A more simplified way of finding the remaining balance of $35,000.00 after taxes have been deducted is to multiply $50,000 by .7 (.7 being 70%) in order to exclude having to find the difference of the annual payment and the combined taxes. The second step is to determine how much interest the invested funds of $35,000 collected over the span of one year. To find out what 6% interest of $35,000 is, we multiplied $35,000 by .06 to get $2,100 (35,000 * .06 = 2,100). The second part of this step is to determine the remaining amount of interest that is collected after taxes have been deducted. The $2,100 of interest is then taxed by 30% making the new interest for the invested funds $1,470.00. To get $1,470, we repeated the same computation mentioned in the previous step by multiplying the interest by .7 (2,100 * .70 = $1,470). $1,470 is then added to $35,000 making the first year‚s invested balance $36,470.00 ($35,000 + $1,470 = $36,470). The same process is repeated to find out the second year‚s invested balance. $36,470 (first year‚s invested balance) + $35,000 (annual payment after deducted taxes) = $71,470. Then, to find the interest you compute the following: $71,470 * .06 = $4,288.20 And to find the interest after taxes have been deducted, you compute the following: $4,288.20 * .70 = $3,001.74 Then to find out the total balance for the second year, you compute the following: $71,470 + $3,001.74 = $74,471.74 This process is repeated according to the new balance of each year until the twentieth year. As the interest grows on each annual payment that is invested, and taxes have been taken into account with the accumulated interest, the final payment received is $1,108,822.28. 2.) To determine the lump sum portion of the project, we first had to deduct 30% of taxes from $1,000,000 leaving the recipient with $700,000. The steps in order to find out how much interest was earned from the $700,000 after twenty years are similar to the annuity portion of the project. To find 6% interest of the lump sum, you multiply $700,000 by .06 ($700,000 * .06 = $42,000). Then you must tax 30% of the interest earned ($42,000 * .70 = $29,400). Next, you add the interest earned with the lump sum ($700,000 + $29,400 = $729,400). This process is repeated for each year until the twentieth year. Second year: $729,400 * .06 = $43,764 $43,764 * .7 = $30,634.80 $729,400 + $30,634.80 = $760,034.80 The accumulated interest growth of $700,000 after twenty years would be $1,592,886.81. 3.) To determine the amount for a lump sum payment that would leave the winner with the same amount as the annuity after twenty years, we first had to cross reference our spreadsheet. We could not find an exact amount; however, the closest amount to the twentieth annuity year of $1,108,822.28 was the eleventh lump sum year of $1,100,634.06. Therefore it would take only about eleven years with the lump sum to reach about the total amount the annuity did in twenty years. 4.) Pros vs. Cons Annuities -Cons- no availability to funds interest earned on smaller amounts of money takes many years to appreciate lower returns on your investments less flexible charged high penalty fees if you take the annuity out early -Pros- steady annual income cannot spend your money all at once taxes are spread out over a larger period of time easier to manage Lump Sum -Pros- receive all your money at once interest earned is greater over time receive more then annuity when invested over time larger amount of assets to work with -Cons- can spend your money faster or all at once all taxes paid immediately pay more taxes harder to manage more discipline required