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How do I determine the interest rate received on annual payments?

Topic closed. 34 replies. Last post 9 years ago by time*treat.

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San Diego, CA
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Posted: March 8, 2008, 2:02 pm - IP Logged

It works exactly like any other loan. They owe you 5.3 million now, but they pay it to you in annual installments of $346,154 totalling $9 million. After the first payment they still owe you about $5 million. A rate of 4.66% compounded monthly would repay the remainder in annual installments of $346,310, which is close enough.  A payment that increases each year definitely complicates the math. They already know the interest rate and do a simple amortization table. Working backwards to figure out what the rate is a collossal PITA, and require a program, and not ust asimple loan calculator. There are two other things you may also want to consider.

1. Why does it matter what the interest rate is when you know exaclty what the actual payment will be?
2. You will be earning that 4.66% interest on the  35 to 42% that  you would lose to taxes if you choose the lump sum. To earn 346k on the $3.445 million you'd have after paying federal taxes you'd need to earn 10% interest.

*** It is my understanding that when taking the lump sum, jackpot winnings are taxed at a 25% rate with no state tax (in California). I am not sure how that changes the math. 

The end result I was looking for was determing what rate I would have to earn to match the rate that they were getting on their annuity.  You state 10%.  Getting a 10% return would seem to involve a lot of risk.  It seems taking the annual payments is better which contradicts my initial thoughts and the thougths of most people on this board whether to take the lump sum or annual payments. 

I would like other thoughts on this.

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    San Diego, CA
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    Posted: March 8, 2008, 2:35 pm - IP Logged

    *** It is my understanding that when taking the lump sum, jackpot winnings are taxed at a 25% rate with no state tax (in California). I am not sure how that changes the math. 

    The end result I was looking for was determing what rate I would have to earn to match the rate that they were getting on their annuity.  You state 10%.  Getting a 10% return would seem to involve a lot of risk.  It seems taking the annual payments is better which contradicts my initial thoughts and the thougths of most people on this board whether to take the lump sum or annual payments. 

    I would like other thoughts on this.

    KY,

    This is becoming more complicated by the minute.

    Did your math factor in that part of the yearly payments would be coming out of the lump sum (the yearly payments won't be all interest, the intial lump sum amount of $5.3 million would be $0 at the end of the 26 years).

     

    The amount of interest earned will be $3,700,000 ($9,000,000-$5,300,000).  That might be a way to determine the number I am looking for.  ( I don't know how though.)

      time*treat's avatar - radar

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      Posted: March 8, 2008, 5:05 pm - IP Logged

      Which ever way you take the payment (lump sum or annuity), you would pay income taxes on it, plus any further income generated by investments* made from it. Future tax rates are unknown and unknowable.

      If you take the 5.3 mil, you're going to pay income tax on that. If you invest what's left, you will pay taxes on any profits taken, at the tax rates in the year in which you took profits.

      If you take the annuity, you're going to pay income tax on it - every year you get a check - at whatever the rate is in that year, plus any profit you made investing any of the previous years' payouts. 

      You can do all types of neat, theoretical calculations on how many ways to get from 5.3mil to 9mil and back, but the real world rates of taxation, inflation, and R.O.I. are constantly in flux.

      To get rate "X" after taxes, you will always by definition need to earn rate "X + something" before taxes.

       

       

      *the exceptions are a) tax-free municipal bonds, & b) sections 29 & 45 investments (where you can get tax-credits)

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

        justxploring's avatar - villiarna
        Wandering Aimlessly
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        Posted: March 8, 2008, 5:11 pm - IP Logged

        I agree with time*treat, which is why I said in my earlier post that figuring all of this out won't apply in the real world. 

        However, I do want to comment on the 25% you mentioned.  The states are required to deduct 25% Federal Tax.  That does not mean you won't owe more.  You would definitely be in a much higher tax bracket. Look at the IRS tax tables for specifics. You would probably also be required to file an estimated tax before you invest all the money so you have the additional amount owed to the IRS.  Of course, most people never tie up all their money anyway, but you might owe an additional $400 or $500K, depending on your deductions. That is why it would be best to consult a tax professional and/or a tax attorney.  If you ever won millions of dollars, you would probably have one on retainer anyway.  Some people think I only recommend taking annual payments because of some earlier threads, but I never do.  I just mention it as an option for those who might not be able to handle the money or even want to bother.

          Coin Toss's avatar - shape barbed.jpg
          Zeta Reticuli Star System
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          Posted: March 8, 2008, 5:44 pm - IP Logged

          No offense towards anyone, but why all these threads and anguish over jackpots that haven't been hit!

          Once upon a time, a lotto player climbed the Himalayas to query the guru, and once at the top, asked about interest rates and investments.

          The guru asked the player, "So how much was the jackpot you hit?"

          The player said they hadn't hit one yet.

          The guru said, "Come back and ask if and when you do".

          Those who run the lotteries love it when players look for consistency in something that's designed not to have any.

          Lep

          There is one and only one 'proven' system, and that is to book the action. No matter the game, let the players pick their own losers.

            time*treat's avatar - radar

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            Posted: March 8, 2008, 5:49 pm - IP Logged

            'cause if we stuck to rational and concrete topics, all the forums would be about as active as the mathematics SleepSleepSleep forum.

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

              Coin Toss's avatar - shape barbed.jpg
              Zeta Reticuli Star System
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              Posted: March 8, 2008, 5:56 pm - IP Logged

              'cause if we stuck to rational and concrete topics, all the forums would be about as active as the mathematics SleepSleepSleep forum.

              True - many moons ago I questioned why the Mystical forum had ten times the traffic of the Mathemnatical forum, but I didn't strip the dream requests out of Mystical when I asked. 

              But, what is "rational" about dirving ourselves nuts over jackpots that haven't been hit?

               How would you spend it, and would you try to remain anonymous are one thing, agonizing over percentages on a make believe are another.

              Just my $.02

              YMMV 

              Those who run the lotteries love it when players look for consistency in something that's designed not to have any.

              Lep

              There is one and only one 'proven' system, and that is to book the action. No matter the game, let the players pick their own losers.

                justxploring's avatar - villiarna
                Wandering Aimlessly
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                Posted: March 8, 2008, 6:01 pm - IP Logged

                I agree with Coin Toss.  If I were interested in figuring out all of the possibilities, I would spend my time on a winning system, not trying to figure out how much interest I'm going to make.  At least with the game itself, there is a constant...and it's fun.   5 years ago just about everyone would say to buy as much FL real estate as you can and flip it every 2 years.  I remember when I was making 18% a year in a money market account in 1980 (although mortgage rates were almost as high.)  I suppose if someone believes he/she is going to be the 1 in 176 million who hits the MM jackpot, then it's worth the effort. But imagine if you went to a CPA or even a bank or investment firm and said "I plan to win the lottery soon, so I need to discuss my options."

                  mjwinsmith's avatar - moon

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                  Posted: March 8, 2008, 6:09 pm - IP Logged

                  I think he's asking for the difference between the annuity and the cash option, if he was to get interest on both amounts from the get go, and then compare them.

                  Since the annuity amount does not exaist as a lump sum, I don't think there can be an answer.  

                  It makes no difference, Lump Sum or Annuity Option, there is an interest rate asssumption that goes into play.

                  For the Lump Sum you have to have an interest rate to compute the "Present Value" of the income stream, that is to say instead of getting the payments over time (26 years) what is it worth TODAY.

                  The interest rate would be tied to something like 10 year treasury notes or bonds or perhaps the Prime Rate of interest in effect today. Bet on something in the 3 to 5% interest range.

                  The Lump Sum that you would get, placed in a bank account and left to accumulate would grow to the Jackpot amount at the end of the 26 years, in theory.

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                    San Diego, CA
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                    Posted: March 8, 2008, 6:18 pm - IP Logged

                    No offense towards anyone, but why all these threads and anguish over jackpots that haven't been hit!

                    Once upon a time, a lotto player climbed the Himalayas to query the guru, and once at the top, asked about interest rates and investments.

                    The guru asked the player, "So how much was the jackpot you hit?"

                    The player said they hadn't hit one yet.

                    The guru said, "Come back and ask if and when you do".

                    Yea...as if these topics aren't trivial.

                     

                    > I wonder what the $275 mega millions winner is doing now.

                    When you win a small prize, Do you spend the entire amount on more tickets, or do you stick to your budget for the night

                    > Would you leave your wife/husband?

                     > 5 + 0 out of 5 + 1 What do you say? Would hitting 5 + 0, coming that close, eventually drive you crazy?

                     > Giving away a winning ticket Would you consider giving a winning ticket as a tip or to a person down on luck?

                     > How will you deal with your money if you shot at the jackpot How will you use your money if you shot at the jackpot

                    > How much will you give to your charity if you win big ?

                     Forgive me for bringing up a topic that would actually have a financial impact on someone's life if they did win a jackpot.

                      ThatScaryChick's avatar - x1MqPuM
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                      Posted: March 8, 2008, 6:29 pm - IP Logged

                      There is no need to apologize JWBlue. Topics like these keep the forum active and some of us actually get to learn something new from them.

                      "No one remembers the person who almost climbed the mountain, only the person who eventually gets to the top."

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                        Kentucky
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                        Posted: March 8, 2008, 9:02 pm - IP Logged

                        Yea...as if these topics aren't trivial.

                         

                        > I wonder what the $275 mega millions winner is doing now.

                        When you win a small prize, Do you spend the entire amount on more tickets, or do you stick to your budget for the night

                        > Would you leave your wife/husband?

                         > 5 + 0 out of 5 + 1 What do you say? Would hitting 5 + 0, coming that close, eventually drive you crazy?

                         > Giving away a winning ticket Would you consider giving a winning ticket as a tip or to a person down on luck?

                         > How will you deal with your money if you shot at the jackpot How will you use your money if you shot at the jackpot

                        > How much will you give to your charity if you win big ?

                         Forgive me for bringing up a topic that would actually have a financial impact on someone's life if they did win a jackpot.

                        They are all topics of discussion and we can decide as individuals which topics are trivial and redundant or worth reading and responding to. How many responses each topic gets might depend on interest or the number of sub-topics started. Three of the topics you mentioned are things the average lottery player could experience and three are things only less than .0000002% of players experience.

                        "Forgive me for bringing up a topic that would actually have a financial impact on someone's life if they did win a jackpot."

                        When we see the Powerball or Mega Millions jackpot is over $200 million, we can expect to see more of the "If I win" topics. And we can expect to see more "Who cares because it only applies to the winner" comments. It's obvious this topic is interesting to you but your feelings shouldn't be hurt because it's less interesting to others.

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                          Posted: March 8, 2008, 11:18 pm - IP Logged

                          KY,

                          This is becoming more complicated by the minute.

                          Did your math factor in that part of the yearly payments would be coming out of the lump sum (the yearly payments won't be all interest, the intial lump sum amount of $5.3 million would be $0 at the end of the 26 years).

                           

                          The amount of interest earned will be $3,700,000 ($9,000,000-$5,300,000).  That might be a way to determine the number I am looking for.  ( I don't know how though.)

                          Yes, it's accounted for. When you pay off a loan you pay interest and principal (unless you've been suckered into a really bad deal where you just pay interest for a few years and still owe as much as when you started). In the example, the lottery would have just under $5 million that they're effectively borrowing from you, since you didn't take the cash. That money would be invested at just under 5%, so it would earn about 250k over the next year, at which time they would pay you  346k. Since they only earned 250 k, the principal will be rduced by about 100k. Each year they'll earn a bit less interest, so your payment will eat up a bit more principal, until the final payment gives you a few bucks interest and the last of the principal. Knowing that the payments required $3.7 million in interest doesn't help figure the interest rate, because you don't know how much principal was invested at any given time until you guess the interest rate and find that the rest of the numbers fit.

                          I also accounted for the federal taxrs you can expect to owe. as others pointed out, 25% is withheld, but winning a jackpot will put you in the 35% tax bracket. Every dollar you get to claim as a deduction will be money you no longer have, so anything less than 35% paid in taxes wil have been spent on something deductible (medical bills, donations, whatever). After losing 35% to taxes you'd have $3.445 million remaining from $5.3 lump sum. You'd need to invest that at 10% to earn 344k each year, about the same as the annuity payment. Of course  the annuity payments would stop after 25 years, but the returns from your investment would continue forever, as long as you leave the principal invested. Unless you plan on dying (or being broke again) before the annuity payments end you have to invest a decent chunk of each payment.

                            Coin Toss's avatar - shape barbed.jpg
                            Zeta Reticuli Star System
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                            Posted: March 8, 2008, 11:30 pm - IP Logged

                            JWBlue

                            I did say just my $.02 and YMMV (your mileage may vary).

                            Every other thread you linked to would have an effect on someone's life if they hit a jackpot, especially the one about leaving your spouse. However, not one of them got into specific interest payments on a jackpot that has not been hit.

                            In one of his books Mario Puzo (The Godfather author) tells of being in an Army hospital in WW II and one of the guys in the ward- a ward for head wounds- convincing himself he had a million dollar idea. He asked all the other patients in the ward what they thought of it and many agreed it was a good idea.

                            Then one said, "Let's go to another ward and ask guys that haven't been hit in the head what thye think."

                            Why did the guy becomes an economist?

                            He didn't have enough personality to be an accountant.

                            Bye, Good Luck.

                            Those who run the lotteries love it when players look for consistency in something that's designed not to have any.

                            Lep

                            There is one and only one 'proven' system, and that is to book the action. No matter the game, let the players pick their own losers.

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                              Posted: March 9, 2008, 3:01 am - IP Logged

                              If the annual payments total $9 million over 26 years and the lump sum is $5.3 million, how do I determine the interest rate received?

                              I don't have a spreadsheet at work (where I do most of my LP interaction), or I would have played with the formula I posted yesterday and given you an estimate.

                              However, tonight I tried just using the Windows calculator and it wasn't so hard.

                              Based on 27 payments, the interest rate falls between 4.7 and 4.8 percent. Not a good return on your investment, imho. Take the cash. Thumbs Up

                              The balls have no memory.