```8 AM Class Group 5
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
less flexible
charged high penalty fees if you take the annuity out early

-Pros-
cannot spend your money all at once
taxes are spread out over a larger period of time
easier to manage

Lump Sum

-Pros-