```8 AM Class Group 4

1. \$1,108,822.28

2. \$1,593,868.25

3. \$695,680.01

4. Lump Sum vs. Annuity
Pros and Cons

Lump sum pros:
- You receive a large sum of money right at the beginning.
- You end up with a larger sum of money at the end of 20 years compared
to if you received     annuity payments, it’s about \$485,000 more than the
amount you would get if you did annuity     payments.
-Accrues more interest over the period of 20 years, with or with out
taxes having to be deducted..

Lump sum cons:
- Pay more in taxes on the interest you earn.
- You pay more taxes right up front.

Annuity pros:
- You pay less taxes on the interest you earn each year.
- You pay less taxes the first year, lump sum you pay 300,000 right up
front, annuity initial     payment you only pay \$15,000 up front.

Lump sum cons:
- You receive less money at the end of the 20 years.
- You still receive only \$700,000 it’s just spread out over 20 years.
(\$35,000 * 20 = \$700,000)
- You get taxed the same amount on the annuity payments as you would
right up front with a lump     sum payment. (\$15,000 * 20 = \$300,000)
- You accrue less interest..

5. Assumptions And Important Information That Was Omitted

There are various assumptions that were made to simplify this assignment
along with important details that were not included. Among these was that
the person receiving either the annuity payments or the lump sum did not
need to use some of the money with in the 20 year span for emergency or
what ever the need would have been. They just keep the money in an
investment account for the 20 years with out touching it. In the real
world many people would save some and use some to be luxuries previous
unattainable with past income.  Also the assignment did not include the
fact that the person winning the lottery did not add additional funds to
their investment from other sources of income. Another detail that helped
to simplify the assignment was that the rate of interest did not change it
stayed the same for 20 years. Which in the real world interest rates on
CDs and other investing accounts are variable and are subject to change at
any moment.

Explanation for question #1:

First what we did was to find out the amount in which the person would get at the beginning of each year if he choose to have 20 annual payments of \$50,000. This was calculated by multiplying the \$50,000 by 25% (Federal income tax) which gives you a product of \$12,500. Next you take the \$50,000 again and multiply it by 5% (Connecticut state income tax) and you get a product of \$2,500. Then  you add both tax amounts to get a sum of \$15,000 which will be deducted from each annuity payment each year. Therefore, you will receive \$35,000 for each year, for 20 years.

Explanation for question 2:

First what we did was find out the amount of tax that will be taken out of the lump sum. So you multiply \$1,000,000 by 25% and 5% for both Federal and Connecticut income taxes. You therefore get a total of 300,000 to be deducted from the \$1,000,000, giving you a lump sum of \$700,000.

The \$700,000 is then invested at 6% each year. For the first year you multiply \$700,000 by 6% giving you \$42,000 in interest. Next you need to have taxes taken out so you multiply \$42,000 by 30% (25% for Federal income tax and 5% of Connecticut state income tax) giving you a product of \$12,600 to be deducted from \$42,000. Therefore you get a net interest of \$29,400. Next you add \$700,000 to \$29,400 together and get an end of the year figure of \$729,400 for the first year, which will then roll over to be re-invested for next year. You continue calculating the interest and taxing the interest for the next 20 years with out adding any new sum of money.

Explanation for question 3:

For this question there are various way to figure out the lump sum that would leave you with the same amount at the annuity did after 20 years. One way that was done was through an excel spread sheet where the cells were link together and to guess and check till the final number came out to be the same as the final number in question 1. The other way that was presented was to do a proportion which looked like this:

Lump sum part 2       =     Lump sum part 3

Ending figure part 2          Ending figure part 1

1,000,000         =            X

1,593,868.25           1,108,822.28

1,000,000 * 1,108,822.28 = 1,593,868.25* X

1.10882228E12/1,593,868.25=X

695,680.0099=X

And when rounded you get \$695,680.01 as your lump sum figure that would equal the same amount as the annuity after 20 years, which is 1,108,822.28.

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