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Can someone help me out with my math?

Topic closed. 11 replies. Last post 9 years ago by KY Floyd.

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whitmansm2's avatar - Lottery-029.jpg
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Posted: August 8, 2007, 10:00 pm - IP Logged

Like most people I wanted to take the lump sum of any major jackpot win.  I started thinking about it the other day, and thought that I was just not thinking things through and thats the last thing I want to do with that huge some of money!  So, I was thinking that maybe annuity is better.  I know everyone has their opinions on which one is better...but I want to know from a mathmatical point of view.  (Don't worry...I understand too, that no one can give me better advice than a financial advisor...but I would still like help with my math if some one can)

Here is the deal...the jackpot is 141million.  The cash amount is 65.6 million.  In my state my average payment, should I accept annuity, would be roughly 3.4 million a year.  They want me to get these payments for the next 30 years to get 141million.  (lets not figure in taxes 'cause that will start getting messy)

I've never been good at math....and I know this really can't be right.... but can someone figure out what my interest rate is on the 65.6mil to get 141mil after 30 years?

The reason is, the way I'm thinking, if I'm getting an 8% return (coughbulls**tcough) then hell yeah I should take the annuity 'cause I can't guarentee an 8% return over the next 30 years.  If I was getting 2.15 (which thats my sucky math) then HOW DUMB WOULD THAT BE?  I know I can get a better rate of return...and that's just me sticking it in my savings account!  So then I SHOULD take the lump sum.

If anyone can help...I'd appreciate it.  Then if you can...can you give me the formula so I can figure it out later?

THANK YOU!!!

No No

Don't cry over spilled milk.  Go milk another cow!!

Stephanie

    JADELottery's avatar - MeAtWork 03.PNG
    The Quantum Master
    West Concord, MN
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    Posted: August 8, 2007, 10:03 pm - IP Logged

    go here

    http://www.usamega.com/powerball-jackpot.htm

    Presented 'AS IS' and for Entertainment Purposes Only.
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      whitmansm2's avatar - Lottery-029.jpg
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      Posted: August 8, 2007, 10:06 pm - IP Logged

      I looked there and that's where I got some of my information....I do appreciate you responding!  But my question...to break it down...is what is my percent rate?  How much am I "making" off of the cash prize if I take the annuity?  What's my return?

      Does that make sense?

      No No

      Don't cry over spilled milk.  Go milk another cow!!

      Stephanie

        RJOh's avatar - chipmunk
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        Posted: August 8, 2007, 10:32 pm - IP Logged

        If you have your savings in a CD that paying 2.5%, banks will automatically renew it with the lower rate instead of the newer improved rate of 4% or better unless you renew it yourself.  You are responsible for getting the best rates for your savings.

         * you don't need to buy more tickets, just buy a winning ticket * 
           
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          whitmansm2's avatar - Lottery-029.jpg
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          Posted: August 8, 2007, 10:51 pm - IP Logged

          lol Now I KNOW I'm not asking my question right!  LOL

          Sorry!  Let me try again.

          To get annuity...they take the cash option....and put it in a bond....right?  You're being paid the dividends every year in an annuity....right?  I'm wondering if my cash option is 65.6 and they put it into a bond so I can get annuity and end up with 141mil, then what interest rate am I getting if my dividends are 3.5mil?

          My math...which again is bad...showed that with the cash option of 65.6mil....and the end amount being 141mil after 30 installments of ROUGHLY 3.5 mil a year...I would be making 2.5% yearly.

          Is this clear as mud, yet?  lol

          No No

          Don't cry over spilled milk.  Go milk another cow!!

          Stephanie

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            Posted: August 9, 2007, 1:36 am - IP Logged

            Your result is definitely wrong, but it's more than a simple math error.  If you invested 141 million at 2.5% the annual earnings would be $3.525 million, so I'm guessing you got the  2.5% figure by starting with the 141 million and an annual income of $3.5 million then rounding the result to 2.5 (3.5/141=.0248). Since the annuity is from an investment of $65.6 million, a $3.5 million pre-tax income is what you'd get from a rate of 5.33% if you didn't collect any of the principal.

            Here's the proper math for equal annual payments if you never collected any of the principal. Collecting $141 million in 30 equal payments means that each pre-tax payment would be $4.7 million, not 3.5. When you claim the prize you'd get the first 4.7 million, which would come out of the cash value of  $65.6 million. That would leave an investment of $60.9 million. Earning 4.7 million from a 60.9 million investment would require an interest rate of  7.72% ((4.7/60.9=0.07718). After 29 years you'd have earned 141 million, but you'd still have the 60.9 million in principal.

            The actual interest rate on PB is a more complicated for two reasons.  First, you don't get the same amount every year. Initially you get a smaller payment and some of the interest is reinvested. Second, at some point you're getting all of the interest earned in that year and you're also getting some of the principal. In the final year you'd get all of the interest on a small amount of principal and all of the remaining principal.

            If you really want to know the actual interest rate the annuity is based on print a copy of the payment schedule, go to an accountant or financial planner and bring a few hundred bucks with you. Personally, I can't see any reason to want an exact answer unless you actually need to choose between annuity and cash. If that happens you'll also have to account for the taxes. The lottery gets to invest the pre-tax cash, but you only get to invest about 60% of that, depending on your state's tax rate.  You could potentially find a better rate than what  PB gets, but you won't get one that's 67% higher, which is what you'd need to earn as much from your 60% as they can get from 100%. Choosing cash over annuity isn't about having more money. It's about having more control and flexibility.

              time*treat's avatar - radar

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              Posted: August 9, 2007, 8:46 am - IP Logged

              A decent college econ book will have a lookup table for this (Interest and Annuity Tables for Compounding).

              If you dig around in Excel or Calc (Financial subcats), the formulas are there, too.

              There are most likely some "plug-in" pages on the web, too. Cool

              In neo-conned Amerika, bank robs you.
              Alcohol, Tobacco, and Firearms should be the name of a convenience store, not a govnoment agency.

                Raven62's avatar - binary
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                Posted: August 9, 2007, 9:09 am - IP Logged

                Annuity

                FV = PMT * [ ( ( 1 + i )N - 1 ) / i ]

                FV = future value (maturity value)
                PMT = payment per period
                i = interest rate in percent per period
                N = number of periods

                Plug in the known values and solve for the unknown value. (In your case: i)

                A mind once stretched by a new idea never returns to its original dimensions!

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                  Posted: August 9, 2007, 11:27 am - IP Logged

                  Annuity

                  FV = PMT * [ ( ( 1 + i )N - 1 ) / i ]

                  FV = future value (maturity value)
                  PMT = payment per period
                  i = interest rate in percent per period
                  N = number of periods

                  Plug in the known values and solve for the unknown value. (In your case: i)

                  That's the formula for the future value of a series of payments, and calculates the total of the payments and the interest earned during the investment period. If you planned to invest each payment from the annuity at a fixed rate of interest that formula would tell you how much you would have accumulated after any given number of payments, if you hadn't withdrawn anything during that period. 

                  By taking the annuity instead of cash you're essentially loaning the principal and collecting mortgage payments until the principal has been reduced to zero, so theproper formual is the same one you'd use for standard loan repayment calculations. A simple web search will turn up thousands of calculators that will happily tell you that  loaning $65.6 million in exchange for annual payments of $4.7 million (actually $391,667 each month, since that's how loans are typically repaid) will result in total payments of $141 million if the interest rate is about 5.96%. To find the right interest rate you'll have to  plug in values until you get the right periodic and total payments, because the calculators are intended to calculate the payment based on a known rate of interest.

                  If it were an annuity with equal payments every year  that would be fine, but PB payments start out small and increase each year. If you make extra loan payments you'll reduce the principal faster and therefore reduce the amount of interest paid, and therfore the total payments. If you miss payments or make smaller payments there will be more principal earning interest and the total interest and total repayment wil be larger. That requires recalculating the values each time the payment schedule is changed. For 30 different payments that's 30 different calculations.That's to calculate payments for a known interest rate of i. Since you can't solve the equation for i, working backwards from the payments to figure the interest rate is a long repetitive process. 

                    whitmansm2's avatar - Lottery-029.jpg
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                    Posted: August 9, 2007, 12:01 pm - IP Logged

                    WOW!  Thank you so much for the information!!!

                    So you're saying that by getting the annuity I would only be getting 5.96% (roughly).  Which I can make more if I take the cash value and invest it myself. 

                    Did I get that right?

                    THANK YOU SO MUCH!!!  This is making more sense.

                    No No

                    Don't cry over spilled milk.  Go milk another cow!!

                    Stephanie

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                      Posted: August 9, 2007, 2:51 pm - IP Logged

                      As best as can be calculated (reasonably) quickly, yes. 6% doesn't even cover the increase in the cost of milk or gas, etc. I'd take the cash, now. It's my money. Use it when I need it. Big Smile

                      In neo-conned Amerika, bank robs you.
                      Alcohol, Tobacco, and Firearms should be the name of a convenience store, not a govnoment agency.

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                        Posted: August 10, 2007, 3:40 am - IP Logged

                        WOW!  Thank you so much for the information!!!

                        So you're saying that by getting the annuity I would only be getting 5.96% (roughly).  Which I can make more if I take the cash value and invest it myself. 

                        Did I get that right?

                        THANK YOU SO MUCH!!!  This is making more sense.

                        No, that's not what I said.

                        If the annuity payments were all the same then it would represent roughly 6% on an investment of $61 million, but the payments aren't equal. The payments for the first  several years are smaller, so that there is more principal invested than if the payments were equal. Because there is more principal the total of the payments is generated with a lower interest rate. As a SWAG I'd put it at about 5.2%.

                        If you didn't have to pay income tax  on the lump sum you could invest the same $61 million yourself, but  you would have to pay tax, so you'd have less money to invest. If you had no state tax you'd still lose 35% to federal taxes, so you'd only be investing $40 million. If PB is getting 5.2% you'd have to earn 8% to get a smuch from your investment. If you also pay state income tax you'd need to get even more than 8%.