```8 AM Class Group 1

Lindsay Bissonnette
James Gerosa
Alyssa Huddleston
Jennifer Rosa
Amy Tran
Math 1070 8:00
6 October 2008
Lottery Annuities
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.

1. The total amount the lottery recipient will have at the end of
twenty-one years being paid \$50,000 annual payments for twenty years,
making 6% interest and 30% taxes deducted is \$1,155,392.82. To find this
value, we used a spread sheet for our calculations to come to our answer.
The first year payment, as seen in row one, of \$50,000.00 gets 30% taxes
taken out. By multiplying \$50,000.00 by .70, .70 comes from 100% minus 30%
to get the remaining amount of money that will be left over once the taxes
are taken out, which is \$35,000.00. The \$35,000.00 then gets multiplied by
.06 for the interest that is made from the money in the account. Then to
find the taxes taken from the interest made you multiply the amount of
interest made, \$2,100.00, by .70 to find the net interest of the first
payment is \$1,470.00. Then to find the Net total of dollars for the end of
year one, the total net interest is added to the net payment to get
\$36,470.00. This amount then gets added in to the net payment of
\$35,000.00 for year 2. This accumulated amount then gets 30% taxes taken
out and then receives 6% interest. The 6% interest made is then taxed by
30%. The remaining amount of interest after tax then gets added into the
total dollars. The total dollars then gets accumulated. Then once the next
payment is received the cycle continues. After the 20 years the amount is
\$1,108,822.28. When this amount is untouched for another year, after that
year the money grows to \$1,115,392.82.

Years	ACCUMULATOR	Payments	AFTERTX	NET PAYMENT	TOTAL DOLLARS	INTEREST	NET
INT.	NET
1		 \$50,000.00 	 \$    0.70 	 \$      35,000.00 	 \$        35,000.00 	 \$
2,100.00 	 \$    1,470.00 	 \$     36,470.00
2	 \$      36,470.00 	 \$50,000.00 	 \$    0.70 	 \$      35,000.00 	 \$
71,470.00 	 \$     4,288.20 	 \$    3,001.74 	 \$     74,471.74
3	 \$      74,471.74 	 \$50,000.00 	 \$    0.70 	 \$      35,000.00 	 \$
109,471.74 	 \$     6,568.30 	 \$    4,597.81 	 \$   114,069.55
4	 \$    114,069.55 	 \$50,000.00 	 \$    0.70 	 \$      35,000.00 	 \$
149,069.55 	 \$     8,944.17 	 \$    6,260.92 	 \$   155,330.47
5	 \$    155,330.47 	 \$50,000.00 	 \$    0.70 	 \$      35,000.00 	 \$
190,330.47 	 \$    11,419.83 	 \$    7,993.88 	 \$   198,324.35
6	 \$    198,324.35 	 \$50,000.00 	 \$    0.70 	 \$      35,000.00 	 \$
233,324.35 	 \$    13,999.46 	 \$    9,799.62 	 \$   243,123.98
7	 \$    243,123.98 	 \$50,000.00 	 \$    0.70 	 \$      35,000.00 	 \$
278,123.98 	 \$    16,687.44 	 \$  11,681.21 	 \$   289,805.18
8	 \$    289,805.18 	 \$50,000.00 	 \$    0.70 	 \$      35,000.00 	 \$
324,805.18 	 \$    19,488.31 	 \$  13,641.82 	 \$   338,447.00
9	 \$    338,447.00 	 \$50,000.00 	 \$    0.70 	 \$      35,000.00 	 \$
373,447.00 	 \$    22,406.82 	 \$  15,684.77 	 \$   389,131.78
10	 \$    389,131.78 	 \$50,000.00 	 \$    0.70 	 \$      35,000.00 	 \$
424,131.78 	 \$    25,447.91 	 \$  17,813.53 	 \$   441,945.31
11	 \$    441,945.31 	 \$50,000.00 	 \$    0.70 	 \$      35,000.00 	 \$
476,945.31 	 \$    28,616.72 	 \$  20,031.70 	 \$   496,977.01
12	 \$    496,977.01 	 \$50,000.00 	 \$    0.70 	 \$      35,000.00 	 \$
531,977.01 	 \$    31,918.62 	 \$  22,343.03 	 \$   554,320.05
13	 \$    554,320.05 	 \$50,000.00 	 \$    0.70 	 \$      35,000.00 	 \$
589,320.05 	 \$    35,359.20 	 \$  24,751.44 	 \$   614,071.49
14	 \$    614,071.49 	 \$50,000.00 	 \$    0.70 	 \$      35,000.00 	 \$
649,071.49 	 \$    38,944.29 	 \$  27,261.00 	 \$   676,332.49
15	 \$    676,332.49 	 \$50,000.00 	 \$    0.70 	 \$      35,000.00 	 \$
711,332.49 	 \$    42,679.95 	 \$  29,875.96 	 \$   741,208.46
16	 \$    741,208.46 	 \$50,000.00 	 \$    0.70 	 \$      35,000.00 	 \$
776,208.46 	 \$    46,572.51 	 \$  32,600.76 	 \$   808,809.21
17	 \$    808,809.21 	 \$50,000.00 	 \$    0.70 	 \$      35,000.00 	 \$
843,809.21 	 \$    50,628.55 	 \$  35,439.99 	 \$   879,249.20
18	 \$    879,249.20 	 \$50,000.00 	 \$    0.70 	 \$      35,000.00 	 \$
914,249.20 	 \$    54,854.95 	 \$  38,398.47 	 \$   952,647.67
19	 \$    952,647.67 	 \$50,000.00 	 \$    0.70 	 \$      35,000.00 	 \$
987,647.67 	 \$    59,258.86 	 \$  41,481.20 	 \$1,029,128.87
20	 \$ 1,029,128.87 	 \$50,000.00 	 \$    0.70 	 \$      35,000.00 	 \$
1,064,128.87 	 \$    63,847.73 	 \$  44,693.41 	 \$1,108,822.28
21	 \$ 1,108,822.28 				 \$    1,108,822.28 	 \$    66,529.34 	 \$  46,570.54
\$1,155,392.82
Totals 						 \$  650,561.17 	 \$455,392.82

2. The amount the winner will have at the end of twenty years when the
winner receives the whole \$1,000,000.00 in one payment is \$1,593,868.25.
To find this we used a spread sheet to organize our calculations of 30%
tax and 6% interest on the money every year for 20 years. The net dollars
after the original tax on the million is \$700,000.00. This then makes 6%
interest which is \$42,000.00 in the first year. The tax then is taken out
of the \$42,000.00 by multiplying by .70, the inverse, to get the
\$29,400.00 net interest. This is then added to the \$700,000.00 to get
\$729,400.00. This then gets accumulated into net dollars and interest is
made and the taxes are deducted for the next 20 years to get the final
total of dollars to be \$1,593,868.25.

Payment 	After Tax	Net Payment	  Net Dollars 	Interest	Net Interest	Net
\$1,000,000.00 	0.7	 \$   700,000.00 	 \$      700,000.00 	 \$     42,000.00
\$  29,400.00 	 \$     729,400.00
\$                -   	0.7	 \$                -   	 \$      729,400.00 	 \$
43,764.00 	 \$  30,634.80 	 \$     760,034.80
\$                -   	0.7	 \$                -   	 \$      760,034.80 	 \$
45,602.09 	 \$  31,921.46 	 \$     791,956.26
\$                -   	0.7	 \$                -   	 \$      791,956.26 	 \$
47,517.38 	 \$  33,262.16 	 \$     825,218.42
\$                -   	0.7	 \$                -   	 \$      825,218.42 	 \$
49,513.11 	 \$  34,659.17 	 \$     859,877.60
\$                -   	0.7	 \$                -   	 \$      859,877.60 	 \$
51,592.66 	 \$  36,114.86 	 \$     895,992.46
\$                -   	0.7	 \$                -   	 \$      895,992.46 	 \$
53,759.55 	 \$  37,631.68 	 \$     933,624.14
\$                -   	0.7	 \$                -   	 \$      933,624.14 	 \$
56,017.45 	 \$  39,212.21 	 \$     972,836.35
\$                -   	0.7	 \$                -   	 \$      972,836.35 	 \$
58,370.18 	 \$  40,859.13 	 \$  1,013,695.48
\$                -   	0.7	 \$                -   	 \$   1,013,695.48 	 \$
60,821.73 	 \$  42,575.21 	 \$  1,056,270.69
\$                -   	0.7	 \$                -   	 \$   1,056,270.69 	 \$
63,376.24 	 \$  44,363.37 	 \$  1,100,634.06
\$                -   	0.7	 \$                -   	 \$   1,100,634.06 	 \$
66,038.04 	 \$  46,226.63 	 \$  1,146,860.69
\$                -   	0.7	 \$                -   	 \$   1,146,860.69 	 \$
68,811.64 	 \$  48,168.15 	 \$  1,195,028.84
\$                -   	0.7	 \$                -   	 \$   1,195,028.84 	 \$
71,701.73 	 \$  50,191.21 	 \$  1,245,220.05
\$                -   	0.7	 \$                -   	 \$   1,245,220.05 	 \$
74,713.20 	 \$  52,299.24 	 \$  1,297,519.29
\$                -   	0.7	 \$                -   	 \$   1,297,519.29 	 \$
77,851.16 	 \$  54,495.81 	 \$  1,352,015.10
\$                -   	0.7	 \$                -   	 \$   1,352,015.10 	 \$
81,120.91 	 \$  56,784.63 	 \$  1,408,799.74
\$                -   	0.7	 \$                -   	 \$   1,408,799.74 	 \$
84,527.98 	 \$  59,169.59 	 \$  1,467,969.33
\$                -   	0.7	 \$                -   	 \$   1,467,969.33 	 \$
88,078.16 	 \$  61,654.71 	 \$  1,529,624.04
\$                -   	0.7	 \$                -   	 \$   1,529,624.04 	 \$
91,777.44 	 \$  64,244.21 	 \$  1,593,868.25
Totals 				 \$1,276,954.64 	 \$ 893,868.25

3. By doing a trial and error process, I found that the lump sum payment
that will receive almost exactly the same amount of money at the end of 20
years as the annuity after twenty years is \$724,898.58. This was done by
guessing and checking the answer through the calculations on the excel
sheet to find interest additions and tax deductions to lead to the lump
sum payment amount.

Lump Sum Payment  	After Tax	Net Payment	Interest	Interest	Taxes	Net
Interest	Net
\$           724,898.58 	0.7	 \$   507,429.01 	 \$            0.06
\$30,445.74 	           0.70 	 \$    21,312.02 	 \$    528,741.02
\$                        -   	0.7	 \$   528,741.02 	 \$            0.06
\$31,724.46 	           0.70 	 \$    22,207.12 	 \$    550,948.15
\$                        -   	0.7	 \$   550,948.15 	 \$            0.06
\$33,056.89 	           0.70 	 \$    23,139.82 	 \$    574,087.97
\$                        -   	0.7	 \$   574,087.97 	 \$            0.06
\$34,445.28 	           0.70 	 \$    24,111.69 	 \$    598,199.66
\$                        -   	0.7	 \$   598,199.66 	 \$            0.06
\$35,891.98 	           0.70 	 \$    25,124.39 	 \$    623,324.05
\$                        -   	0.7	 \$   623,324.05 	 \$            0.06
\$37,399.44 	           0.70 	 \$    26,179.61 	 \$    649,503.66
\$                        -   	0.7	 \$   649,503.66 	 \$            0.06
\$38,970.22 	           0.70 	 \$    27,279.15 	 \$    676,782.81
\$                        -   	0.7	 \$   676,782.81 	 \$            0.06
\$40,606.97 	           0.70 	 \$    28,424.88 	 \$    705,207.69
\$                        -   	0.7	 \$   705,207.69 	 \$            0.06
\$42,312.46 	           0.70 	 \$    29,618.72 	 \$    734,826.42
\$                        -   	0.7	 \$   734,826.42 	 \$            0.06
\$44,089.58 	           0.70 	 \$    30,862.71 	 \$    765,689.12
\$                        -   	0.7	 \$   765,689.12 	 \$            0.06
\$45,941.35 	           0.70 	 \$    32,158.94 	 \$    797,848.07
\$                        -   	0.7	 \$   797,848.07 	 \$            0.06
\$47,870.88 	           0.70 	 \$    33,509.62 	 \$    831,357.69
\$                        -   	0.7	 \$   831,357.69 	 \$            0.06
\$49,881.46 	           0.70 	 \$    34,917.02 	 \$    866,274.71
\$                        -   	0.7	 \$   866,274.71 	 \$            0.06
\$51,976.48 	           0.70 	 \$    36,383.54 	 \$    902,658.25
\$                        -   	0.7	 \$   902,658.25 	 \$            0.06
\$54,159.49 	           0.70 	 \$    37,911.65 	 \$    940,569.89
\$                        -   	0.7	 \$   940,569.89 	 \$            0.06
\$56,434.19 	           0.70 	 \$    39,503.94 	 \$    980,073.83
\$                        -   	0.7	 \$   980,073.83 	 \$            0.06
\$58,804.43 	           0.70 	 \$    41,163.10 	 \$ 1,021,236.93
\$                        -   	0.7	 \$1,021,236.93 	 \$            0.06
\$61,274.22 	           0.70 	 \$    42,891.95 	 \$ 1,064,128.88
\$                        -   	0.7	 \$1,064,128.88 	 \$            0.06
\$63,847.73 	           0.70 	 \$    44,693.41 	 \$ 1,108,822.29
\$                        -   	0.7	 \$1,108,822.29 	 \$            0.06
\$66,529.34 	           0.70 	 \$    46,570.54 	 \$ 1,155,392.83

4.
Lump Sum Payments-	Pros: The initial payment is more. You accrue more
interest. You end up with more money in the end.
Cons: More taxes are taken out.
Annuities- Pros: You don‚t spend all your money at once. You don‚t accrue
as much interest.
Cons:Make less money in the end of the 20 years compared to the lump sum
payment.

5.       Some assumptions that we made were that this person did not spend
any money over the 20 year period. Also we didn‚t take into account
inflation. Another assumption we made was that the person used only one
bank account. They could have put the money into different accounts with
different interest rates. We also made the assumption that the interest
rates didn‚t change during the 20 years. We also assume for simplistic
purposes that you receive the payment on January first of each year and
the interest is totaled and collected on December thirty-first.
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