# Is Weekly Lottery Money Really a Guaranteed Million?

Pamela is a member of The Motley Fool Blog Network -- entries represent the personal opinion of the blogger and are not formally edited.

When it comes to retirement and stock market investing, most people that I know pick a plan from their employer’s 401K program, get automatic deductions from their paycheck, and don’t really think about it anymore.  At the same time, many of these same people actively participate in buying lottery tickets; some even spend a lot of time choosing their “winning numbers.”

The reason I bring this up is because I was reading a good book recently that had a quote about lotteries and investing that really caught my eye: “If a young person with a \$10/week lottery habit could forgo the fantasy and invest the weekly \$10 in a typical mutual fund that returns an annual 10%, becoming a millionaire in 30 years will be guaranteed” (Rothchild, “The David Dynasty”, 2001).

While it was a good book on the Shelby Davis family and their investing style (buy and hold), this lottery statement did not seem correct to me, so I decided to investigate.

I first looked into the lottery aspect of it.  Spending \$10 a week on lottery tickets for 30 years means you spend \$15,660.  In most lotteries, the odds of winning over a million dollars are small.  For example, with the U.S. Powerball lottery, the odds of winning the big jackpot are approximately 1 in 80 million.

 Powerball Lottery Odds of Winning: Match 5+ Powerball = 1:80,089,128 Match 5 = 1:1,953,393 Match 4+ Powerball = 1:364,042 Match 4 = 1:8,879 Match 3+ Powerball = 1:8,466 Match 3 = 1:207 Match 2+ Powerball = 1:605 Match 1+ Powerball = 1:118 Match Powerball    = 1:74

In considering the odds, a likely scenario is that you would win the Match 4 once, Match 3 approximately 32 times, and the Powerball by itself 2 times (or some other similar combination).  This particular combination yields winnings of \$332.  However, you lost \$15,328 (or you may prefer to say that you donated this money to a cause – although I don’t think you can get a tax deduction for this).

LOTTERY:  EARN \$332 - SPEND \$15,660 = LOSS OF \$15,328

Now what about if you invested that money?  The quote mentioned that investing in a mutual fund with an annual return of 10% would guarantee that you would become a millionaire. Since many brokerage firms require your first mutual fund investment to be a minimum of \$2,500, with subsequent automatic investments of a minimum of \$250, you really can’t invest until you save up that first \$2,500.

You decide to follow this strategy and stick your \$10 a week in a jar until you reach the necessary amounts, with the first being \$2,500 (which occurs at the end of 250 weeks).  You then have to wait another 25 weeks for each subsequent \$250 investment.  Assuming compound investing every 4 weeks at the 10% annual return, you will find that after 30 years, you have \$89,593.  This is a far cry from a million dollars.

What about if you invested the money every time you got \$2,500 saved in your cup in a particular stock instead?  To use real numbers, I will assume you started your \$10/week savings in January of 1982.  You would be able to invest \$2,500 in October 1986, July 1991, May 1996, December 2005 and September 2010.  I went ahead and picked five stocks with no dividends that you could have invested in that were around in the 1980s and 2011:  Apple (NASDAQ: AAPL), Berkshire Hathaway (NYSE: BRK-A), Cincinnati Bell (NYSE: CBB), CACI International (NYSE: CACI), and Farmer Brothers (NASDAQ: FARM)

Putting all of your money in only one stock can be risky (refer to the table below).  With Apple, Berkshire Hathaway and CACI, you would have done well (\$486,104, \$159,661, and \$236,533, respectively), but with Cincinnati Bell (\$6,504) or Farmer Brothers (\$11,489), you might have wished that you spent that money on lottery tickets.  For comparison purposes, I also calculated the 10% annual return in terms of the \$2,500 investments (instead of \$2,500 for the first and \$250 afterwards); in this case, with the mutual fund, you would have approximately \$77,892.

 Value on Dec 30, 2011, After Saving \$10/Week and Investing When Reaching \$2500 for 30 Years (\$15,660 Invested) Value on Dec 30, 2011, when Investing \$15,660 on Day 1 with No Subsequent Investment AAPL \$486,104 \$763,873 BRK-A \$159,661 \$673,717 CBB \$6,504 \$1,726 CACI \$236,533 \$654,173 FARM \$11,489 \$29,146 10% Annual Return Mutual Fund \$77,892 \$310,949 Lottery -\$15,328 -\$15,328

Consequently, none of my calculations were over one million dollars.  So where was that book quote coming up with the million dollars?  Maybe if you had \$15,660 in the bank on that first day that you spent the first \$10 for the lottery ticket and you invested that entire \$15,660 on day 1, leaving it in for 30 years at the 10% annual return? Maybe that would be how you would have over a million? But there was no million with that situation either; it only yielded about \$310,949.  However, most people that I know that are buying weekly lottery tickets don’t have \$15,660 at one time to spend on anything like this.  They are spending the \$10/week, because that is what they have.  Regardless, I’m still baffled as to where the ‘guaranteed’ million would come from.

What does this tell us about whether we should buy a weekly lottery ticket or not? Well, no one can really predict the future, but the results show that the odds are much better if you would invest in the stock market than in the lottery ticket.  If you buy the lottery tickets, you may only have \$332 at the end of 30 years.   If you invest the time you spent in selecting lottery numbers and buying lottery tickets into researching companies and picking stocks, or at least a mutual fund, the odds are that you would do much better than you would with the lottery.  And no, you are not guaranteed a million dollars with a mutual fund with \$10 weekly investments, even at 10% annually.

Lucy2007 owns shares of AAPL. The Motley Fool owns shares of Apple. Motley Fool newsletter services recommend Apple. Try any of our Foolish newsletter services free for 30 days. We Fools may not all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors. The Motley Fool has a disclosure policy.If you have questions about this post or the Fool’s blog network, click here for information.