Is it Better to Take the Lump Sum or Annuity if You Win the Lottery?

[Gomar]

http://thewitlessinvestor.wordpress.com/2012/03/27/you-won-the-lottery-lump-sum-or-annuity/

"If I invested my lump sum of $259 million today, and earned on average 10% from my investment, then is 26 years,... I will have around $3 Billion."

Besides a grammar error: "then >is = IN< 26 years"

How in the world do you get from $259m to $3B in just 26 years?! That is x11.5 growth. Not even the Trumpster is that smart. Or has he taken a page from a ponzi schemer who went to jail?

Nevermind that $363m / 26 annuity is $14m annually. No one could match 4% the feds guarantee; thus annuity is a much better choice.
Plus, if current investments are bad, you just switch when you get the next check.
And, ifcourse, you can't blow all your dough.
It was said that the last PB jackpot winners of $570m who took the lump sum saved $90m over 30 years. Huh?
Less money = less taxes. I don't see any savings here.

 

[Jimmy Snyder]

1.1^26 = 11.9

 

[russ_watters]

So...closer to $3.1 billion...

Welcome to the wonderful world of compounding interest!

I've written a detailed post on a related piece of this issue I'll be posting in the next couple of days. People just don't get the power of compounding interest in investing. You can get 5x your money back from modest investments for retirement.

 

[256bits]

With 10% return on investment, roughly every 7 years your money doubles. After 3.75 doublings,$259 M turns into $3 billion.

 

[Gomar]

1.1^26 = 11.9

ok, so are you saying a 1.1% interest rate is a good investment?
Lump sum is supposed to beat annuity rate, not be less.

 

[lisab]

ok, so are you saying a 1.1% interest rate is a good investment?
Lump sum is supposed to beat annuity rate, not be less.

No, 1.10 is principal + 10% interest, or 1 + 0.10 = 1.10

 

[Pythagorean]

ok, so are you saying a 1.1% interest rate is a good investment?
Lump sum is supposed to beat annuity rate, not be less.

1.1 = 100% + 10% = principal invested + average earned interest (given by OP)

 

[jtbell]

Of course, most people don't start out with a lump sum and let it sit and grow for 26 years. They start with practically zero, (hopefully) contribute to it steadily over the years, and the returns pile up on top of that.

I've posted this graph before, but now that it's the end of the year this is a good time for an update. It's the relative value over the years of my tax-deferred 403b plan (similar to a 401k but for non-profit organizations like most colleges and universities). The TIAA portion is an annuity which is based mostly on bonds and similar things. It's "guaranteed" not to lose value, and has an interest rate that depends on what years the contributions were made in; I'm getting about 4% overall right now. The CREF portion is a broadly based stock mutual fund.

I think I started with annual contributions (including employer contributions) around 10% of my salary. I've increased my contribution regularly, and made one last big increase a couple of years ago, as I make a final push towards retiring in a few years. I've always split my contributions 50/50 between TIAA and CREF, and have never shifted money from one account to the other.

One graph has the earlier years adjusted upwards so everything is in current dollars.

(No, I'm not going to say what the vertical scale is. The graph unit is not a round number.)

 

[Drakkith]

My very rough calculations put me at around $20,000 invested in the last 6-7 years in my TSP (kind of like an 401K i think), and I now have about 30,000 in it from the returns + investment. Not too bad. And that's my first 7 years. I have about 35 more years, or about 5 more 7-year blocks for all that to keep doubling and whatnot before I can start pulling from it.

 

[Jimmy Snyder]

ok, so are you saying a 1.1% interest rate is a good investment?

No, that's not what I am saying. If you invest your principle at 10% interest, that means that at the end of the year you will receive 100% of the principle back plus another 10% of the principle as interest. All together, you will receive 110% of your principle. The Latin words per cent literally mean divided by 100, so 110% means 110 divided by 100, or 1.1. Notice that there is no percentage sign on the 1.1. In order to find out how much money you would have at the end of the year, you can multiply the money you invested at the beginning by 1.1. So if you invested $259 million at 10% then at the end of the year you would have $259 million x 1.1 = $285 million. At the end of the second year you would have $285 million x 1.1 = $259 million x 1.1 x 1.1 = $313 million. That is $259 million x (1.1)^2. At the end of 26 years you would have $259 million x (1.1)^26 = $3087 million = $3 billion 87 million. Here are the numbers year by year.

0 259     10 672      20 1742
1 285     11 739      21 1917
2 313     12 813      22 2108
3 345     13 894      23 2319
4 379     14 984      24 2551
5 417     15 1082     25 2806
6 459     16 1190     26 3086
7 505     17 1309
8 555     18 1440
9 611     19 1584

A simpler calculation is the one I gave: $259 million x 1.1^26 = $259 million x 11.9 = $3082 million.

 

[russ_watters]

(No, I'm not going to say what the vertical scale is. The graph unit is not a round number.)

It would be useful if you made the vertical scales go from 0 to 1 to show the difference between the the two graphs though. The way you posted them, they look almost identical!

Also, is it possible to show your contributions on the same graphs to show what the actual growth was? It is impossible to see from those graphs how much is growth due to contributions and how much is growth due to interest.

Also, may I ask how you got those graphs? Do you manually track this or does your investment company provide you the historical data?

 

[Jimmy Snyder]

The only thing that graph shows is that total = TIAA + CREF.

 

[jtbell]

It would be useful if you made the vertical scales go from 0 to 1 to show the difference between the the two graphs though. The way you posted them, they look almost identical!

They use the same vertical scale. I too was surprised that they look so similar. I took the quarterly CPI values from the BLS website (I think) and multiplied each nominal dollar value by (CPI now)/(CPI then). The CPI values range from about 105 at the beginning of 1985 to about 230 for the latest one.

Also, is it possible to show your contributions on the same graphs to show what the actual growth was? It is impossible to see from those graphs how much is growth due to contributions and how much is growth due to interest.

As it happens, I maintain a separate graph that shows total contributions and total value. The scale is the same as the other two.

Also, may I ask how you got those graphs? Do you manually track this or does your investment company provide you the historical data?

I've kept all my quarterly TIAA-CREF statements, and entered the data by hand from those. It took me an hour or two, one rainy afternoon a few years ago. I don't have the 4th quarter statement for this year yet, so the last data point is an estimate based on this quarter's contributions, the current price per CREF share, and the interest rate that I've been getting on TIAA.

 

[russ_watters]

They use the same vertical scale. I too was surprised that they look so similar.

Hmm... Thinking about it more, I guess that makes sense. If you index both end points to today's dollar and work the inflation backwards, the graphs will deviate as you go backwards toward the start. But since both started at zero anyway, it is tough to see. However you can look at the 2013 values and see they are identical while the 1997 values are not.

As it happens, I maintain a separate graph that shows total contributions and total value. The scale is the same as the other two.

Thanks. So this shows that your investment is worth almost exactly twice what you have put into it. Doubling time is hard to figure in a scenario where you are always contributing to the fund -- which was part of your point in your first post.

I've kept all my quarterly TIAA-CREF statements, and entered the data by hand from those. It took me an hour or two, one rainy afternoon a few years ago.

I should do something similar. I've been tracking my income in that way, but haven't put my investments in. I just got a 401K 4 years ago though.

 

[Gomar]

A simpler calculation is the one I gave: $259 million x 1.1^26 = $259 million x 11.9 = $3082 million.

ok, so could you please point me in the direction of a stock, mutual fund, bond, TBill, etc. that pays 10% annual return. Is it gold, silver, platinum? Are coins and paintings a good investment? I hear Jackson Pollock, Warhol, Basquiat are selling at auctions like hot cakes.

Oh, I got it, real estate will make me a monthly income of $30k... atleast that's what those infommercials say. Just find a depressed property, and flip it for a 75% mark-up! Got it!

But really, you can't beat 4% annual return _guaranteed_ by the state; thus, making annuity a far safer choice.

 

[Jimmy Snyder]

ok, so could you please point me in the direction of a stock, mutual fund, bond, TBill, etc. that pays 10% annual return. Is it gold, silver, platinum? Are coins and paintings a good investment? I hear Jackson Pollock, Warhol, Basquiat are selling at auctions like hot cakes.

Oh, I got it, real estate will make me a monthly income of $30k... atleast that's what those infommercials say. Just find a depressed property, and flip it for a 75% mark-up! Got it!

But really, you can't beat 4% annual return _guaranteed_ by the state; thus, making annuity a far safer choice.

Throughout stock market history, the average yearly return for periods of 25 years or longer has been around 9-10%. Here we mean total return -- i.e., including dividends.

http://observationsandnotes.blogspot.com/2009/03/average-annual-stock-market-return.html
I have some of my money in a variable annuity that pays a guaranteed 7% a year and actually pays more than 7% in good years. Last year it paid 12%.
1.04^26 = 2.77
1.07^26 = 5.81