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. Next we calculated the interest and taxes on the interest for each year while keeping a running balance of each year using an excel spread sheet. At the beginning of year one you receive your first $35,000 payment which is invest at a 6% interest rate, therefore you multiply $35,000 by 6% which gives you a product of $2,100. Next you need to find out the amount you must pay in taxes on the interest you earn for that year. You multiply the interest, $2100 by 30% (25% Federal tax plus 5% state tax) and end up with a product of $630. Then you subtract $630 away from $2,100 because that is the amount of taxes you must pay on the interest you earn that year. This give you a net interest of $1,470.00, which is then added to the $35,000. Giving you $36470 as your end of the year figure which will be carried over into the next year to be re-invested earning 6%. For the next year, you take what your ending figure was for the last year and add another annuity payment of $35,000, which gives you $71470 for year 2, this money will then earn 6% interest.. So the interest for the second year is $4,288.20, which is then taxed by 30%, deriving a product of $1,286.46 which in turn will be subtracted from your interest, giving you a net interest of $3,001.74. Then you add the interest to the beginning of the year figure, $71,470.00, and you get a sum of $74,471.74. Then you add $35,000 to 74,471.74 and continue you calculating the interest, taxing the interest, and re-investing the rest and adding annuity payments for the rest of the 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.