Let me assure you that before you read this topic, there is a financial benefit to this
article and it’s not what many think. First, it is not who is right or wrong, and it’s not
about become very wealthy and do lots of good in society. As I say, do lots of good to the
world, and I’m asking you not to be spending on self-ego.

So, here we go. You are to get a job offer and you have 20 seconds to decide what option
you are going to take. You been offered a job by a very wealthy family to drive them to Las
Vegas and show them all the shows in Las Vegas. You tell them it will take a month to do
it. Now they give you three options to get paid.

1-        One million dollars for the 31-day tour,
2-        $1,000 dollar a day for 31 days,
3-        And finally one penny per day and double the penny every day for 30 days.

Be honest with yourself. And give yourself 20 second to decide. BZZZZZZZ, time up.

Remember this is not about being right. Write down your answer and save it. Now read
about how many versions there are and finally an opportunity to learn and put to practice
the real meaning hidden inside the math question about a penny a day. The answer from
the Security Investments Company or the SIC answer.  Copyright © 2012 Roy S. Idrach

Let’s see how is possible.
Much has been said about a penny a day for many years. When I was a kid we use to play
the game by asking those who did not know the answer. Little we did know that we either
did not knew the real and exact answer, and today as an adult it took me years to find
anything of value into the question. Of how much is a penny a day double it for 30 days.
There are many versions, here just a two of them.
Versions:
1-   You have been offered a job for $1,000,000 for a month’s work, or to get paid a penny the first day and double it  
every day for 30 or 31 days.

2-   This version is from King Arthur’s times, where a rich lady asks how to pay one of her servants. She is told to pay by
giving two grains of rice the first square of the chessboard and double it every time she fills each square on the
chessboard. This will take 64 squares to be filled with a grain of rice that has been doubled every time a deposit is
made. She find out that there was not enough rice in the kingdom to fill the board.

To add to the problem, everyone seems to have an answer of how it is to be done to come with the correct answer.

Here I explain many versions and combine it with the correct answer. The complete tables are at the end of the article.
This version starts with day zero. To me, there is problem here; there is no such thing as day zero. If there is a day zero, it
must be yesterday. By using day 0 we actually have 31 days. In this case, you’ve been overpaid by $5.3 million or you’ve
been shortchanged by 5.3 million since 31 days equals $10,737,418.24. Notice the $1,000 a day results don’t match the days.


Table -1  first 8 days                                                        Table -1 Last six days












Then comes the second version, and it’s not exactly correct, either.

Here is why: If I pay you one cent on Monday and Tuesday, I have to pay double the amount of the day before. So on the 2nd
day, you are paid two cents and on the third day you are paid four cents, and so on. Let’s see how it goes.

Table - 2  first  seven days                                                     Table - 2 last six days














Here we find that by doubling the penny every day from one to 2, 4, 6, 8 and so on, we arrive at the end of 30 day to a grand
total of $5.3 million dollars. And if you were paid at the rate of $1,000 per day each day, the total matches the days.  Some
people come to this answer by using this formula; S = (first term)(1-r^n)/(1-r)

Easier way to do with a calculator.

I come to the same answer by using a calculator in a more simple method. Since 2x2=4 and is the total of the 3rd day, I plug in
2x2 on the calculator, press = and get 4 cents. I know I’m on the 3rd day pay and press the = key 27 more times for the
remainder of the 30 days and come to the same total: 5,368,709.12.
Try it.

Now our version:
We found only one place on the Internet that comes to the correct answer and agrees with us.

If we take a careful look at this problem, we find an interesting answer. Let's look at what happens in the first few
days. The first day there is no double pay. From the second day on, we must double by the previous day’s pay. Day
2 (.01x 2=2), Day 3 (.02x 2=4), and so on.

Our version adds something extra: If we are paid by the day, we get one cent on day one, two cents on day two, four
cents on day four,and continue for 30 days. As we add the pennies we’ve been paid, we find exactly how much has
been paid (
shown in Addition of money paid daily ).

On day one, one penny has been paid. On the second day, three pennies have been paid. By the 5th day, 31 cents
has been paid. As we can see, the 4th column shows a payment of 16 cents, when in reality the actual total payment
received is 31 cents. Taking this into consideration, by the end of 30 days, there is going to be more than 1 million
dollars for the month’s payment and more than $5 million for the penny doubled every day option.












We need to see that on Penny double daily column the payment increases the salary 100 percent for  each new day
worked. The reason we don’t see it is because the previous day is multiplied by 2.( or by 100% of  previous day
pay) This regular pattern is known as geometric series. A geometric series is a constant ratio between consecutive
terms. In this case we always multiply by two or increase the pay by 100% each day.

                     AS WE JUMP TO THE FINAL DAYS WE FIND OUT:
















As we can see, when adding the daily payment we find a total new amount for either 30 days or 31 days, and the only
salary remaining the same is the $1,000 per day.

So, who is right? If you are paid daily and the previous day’s pay is doubled, our version tells us that we must be careful to not
give a quick answer when we accept terms, especially when is no way to calculate mentally. The term of $1,000 a day for 30
days is the sum of 30 days at $1,000 is easy, and the one million for the 30 days is even easier. We tend to go with sure bid.
Our version takes a daily payment and adds it to each day we get paid, to come the actual daily accumulation of pay.

WHAT CAN WE LEARN FROM THIS ARTICLE?

There is lot of information hidden inside the question of a penny a day for 30 days. The answer is compounding. It’s
clear that no one can maintain a 100% daily payment for a long period of time. We can learn a lot from this lesson.
While it is not realistic to double your money on a daily basis, it is realistic and possible to do it if we expand the
time frame.

So, how is this accomplished? Let me give you two examples.

First, we want to use the rule of 72. The rule of 72 said that in order to calculate the number of years it takes to
double your money in an investment, divide 72 by the rate of percentage gained on the investment.
Example: How many years to double my money in a savings account if the bank pays .025 (a quarter of 1% a year).
So, if we take .72 / (divide) by .025 ( interest ), it will take approximate 28.8 years.

Now let’s do it with 8% a year:
.72 / .08 = 9. It will take about nine years to double your money. Remember, this is just an estimate. The real time is
eight years plus a few months, and the real formula is not the scope of this article. For those who are interested,
here it is: ( PV = FV / (1+r) n ). But before you get the rundown formula, don’t forget that a rate of return on an
investment is the reverse of rate of interest on a loan.  

When making a loan, a bank is also looking at how long it will take for them to double their money. However, you
have an advantage. They are regulated and you are not. Now, the two investments have something in common. The
bank runs the risk of the loan being in default and losing the depositor’s money. You, the investor, run the same risk
of losing your money, but with the advantage of selling your investment and cutting short the bleeding, while the
banker cannot.

Example: You have about $2,500 to invest—your PV (Present Value)—and you want to know how much you’ll get
in five years. To determine your FV (Future Value) at 10% a year for five years: (1+0.10)5. So, your PV $2,500 x
1.10 to the power of 5, will give you your FV in 5 years.

Another way is: $2,500 x 1.10 x 1.10 x 1.10 x 1.10 x 1.10 = FV, your future value. With a regular calculator, just
plug in 2,500 * 1.10*1.10*1.10*1.10*1.10 then = and you get your answer of $4,026.275. So: $2,500 x 1.10 =
$2,750 first year; $2,750 x 1.10 = $3.025 second year; $3,025 x 1.10 =$3,327.50 third year; $3,337.50 x 1.10 =
$3,660.25 fourth year; $3,660.25 x 1.10 = $4,026.28 for the fifth year.

In other words, $2,500 will grow to $4,026.28 in five years. And if you invest it at 10% for 6 years, you will almost
double your money to $4,428.90, and it will double in 7 years and 2 months, approximately.

You probably wonder why I spend so much time on this. I’ll tell you why. I need for you to change your habit of
investing and see that it’s possible to double your money in a much shorter time frame than you think.
I know people who work 4 hours a day and make $250,000 day, day in and day out, just by investing, I was
astonished when I saw what a single man was doing with just a click of a mouse. More astonishing is to know that it’
s normal for some bankers on Wall Street to make millions a day, day in and day out. I’m just a small amoeba in a
vast sea of super-large whales, as you will learn next.

                   INTERMISSION TIME  ( Is time for a video. )

Before we get to example two, take a rare look inside the secretive world  of "high-frequency trading,"  I want you to
see how people makes millions daily with fraction of pennies. Similar as what we just discussed.
                            

                                              
 From: CBS 60 minute on YOU TUBE
           
                          http://www.youtube.com/watch?v=WstJM_aNSj8
                                                    High Frequency trading video

















Example two: Now let’s get out of the bank .025% interest, and let’s take our money and invest it in stock. You buy
100 shares @ $5.00 a share, a $500.00 investment plus $7.00 commission. The stock goes up 50 cents in a week;
you just made $50.00 or 10% in one week. If you can make $50 every week for ten weeks, you will double your
money. Now you have $1,000.

Going back to the penny-a-day question, we can see that it may be difficult to double your money every day at
$500.00 a day. It is now possible to do it by extending the time into 10 weeks. How much is it in a year? 10% every
week equals 100% every ten weeks, and in 50 weeks, almost a full year, you have 500% return on your investment.  
Here, we don’t even have to use rule of 72 because 10% in a week is much more than 10% a year. However, if you
were to make 10% a year on a $500 investment, it will take a little over 7 years to double your investment. But here,
you’re doubling it every 10 weeks. It’s just a matter of how much we can invest.

Some people can really invest BIG and make millions daily as you will see later on this page.  

This brings us to one of the most important secrets: the secret of compounding; in short, getting money that makes
money over money. Here is how compounding earnings or interest works.
To understand compounding interest we need to see how this concept works. This means that the interest you
earned last year on your savings account also will earn interest this year. This powerful force was described by

Albert Einstein as principal of compounding
: When you invest in the form of savings or in the form of buying
stocks or mutual funds that are manifested by the effect of compounding interest in a savings account or a dividend
paid by the stock company or mutual fund where you invest.

Why is it so powerful, according to Mr. Einstein?
Look at it this way: You are being paid interest on the original principal amount invested; you are paid interest on
previous years’ interest or accumulated previous interest. Not bad!
Think about this just like the penny-a-day question, allowing time for the rate at which you earn interest to speed up
and become just like a small snowball. As it accelerates, it starts growing bigger and bigger at a faster speed, just
like the last few days of the penny-a-day example. At the end of this article, I’ve made a graphic picture to visualize
what those people who make millions daily are doing. This will open your eyes big time.
While you here try the
compounding interest calculator and see what Mr. Einstein is about.

Take, for example, one of the mutual funds we own. It pays about 8% a year. The 8% is paid in a form of more
dividends every month. This payment is turned immediately into more shares of the mutual fund. In short, we are
getting FREE SHARES. Next month those shares will earn dividends together with the other shares, with the
exception that these shares are free. And every month the same cycle repeats, and more shares come in—in the
form of dividends—and are turned into even more shares. At the end of 8 years, the initial investment will double.

A mutual fund with 20% a year return for each $1,000 invested will look like the following figure.
Let me tell you, this is not impossible, since many fund managers have been doing it for years. (All figures are
approximate, since the importance of this subject is to provide the information and not to be a perfectionist.)

A $20,000 investment will turn into $140,000 in ten years, and a million plus in 20 years. Notice the black line from
$1,000 move into the red line in 7 years, and 300% in the next three years. What you think the investment is going to
do in the three years,
no words can explain more than this graphic. Get involved. Do it!

Study the graphic below carefully and then do a favor if you like this article please
click here  and let us know what
you think. But before you do, see the video from CBS 60 minute on YOU TUBE.  Here is a simple interest
compounding calculator for you to practice. It will show the growing rate schedule for each year.

Practice: 1 - You invest $10,000 at 10%  and zero monthly deposits at age 20. In 42 years when you retire, how
much you will have? See the power of compounding at work.
2- You invest $100 at 10% and monthly deposits of
$100 for 42 years. When you retire at  age 62 or earlier how much you will have? You will find that $100 a month
consistently do more than a large amount and nothing done thereafter.
Security Investments Company  Since 1972
Day        Payment of            Salary 1000 /day  
0                      $0.01                    $1,000
1                      $0.02                    $2,000
2                      $0.04                    $3,000
3                      $0.08                    $4,000
4                      $0.16                    $5,000
5                      $0.32                    $6,000
6                      $0.64                    $7,000
7                      $1.28                    $8,000
Let’s jump to: day 25-30
25             $167,772.16             $25,000
26             $335,544.32             $26,000
27             $671,088.64             $27,000
28             $1,342,177.28          $28,000
29             $2,684,354.56          $29,000
30             $5,368,709.12          $31,000
Day     Penny double daily       $1,000 a day

1                     $0.01                   $1,000
2                     $0.02                   $2,000
3                     $0.04                   $3,000
4                     $0.08                   $4,000
5                     $0.16                   $5,000
6                     $0.32                   $6,000
7                     $0.64                   $7,000

Day     Penny double daily    $1,000 a day
25              $167,772.16            $25,000
26              $335,544.32            $26,000
27              $671,088.64            $27,000
28              $1,342,177.28         $28,000
29              $2,684,354.56         $29,000
30              $5,368,709.12         $30,000
Day   Addition of money                 Penny double daily       $1,000 a day
paid daily
1                                1   =  0.01            1x.01 = 0.01                $1,000
2                           1+ 2   =  0.03            1x.02 = 0.02                $2,000
3                        1+2+4   =  0.07            2x.02 = 0.04                $3,000
4                    1+2+4+8   =  0.15           .4x.02 = 0.08                $4,000
5              1+2+4+8+16   =  0.31           .8x.02 = 0.16                $5,000
6       1+2+4+8+16+31    =  0.63         0.16x 2 = 0.32                $6,000
7                                         1.27                        0.64                 $7,000
8                                         2.55                        1.28                 $8,000
Day          Addition of money         Penny double daily        $1,000 a day
  paid daily

24               $167,772.15                  $ 83,886.08                 $24,000
25                 335,544.31                   167,772.16                 $25,000
26                 671,088.63                   333,544.32                 $26,000
27              1,342,177.27                   671,088.64                 $27,000
28              2,684,354.55                1,342,177.28                 $28,000
29              5,368,709.11                 2,684,354.56                $29,000
30
           10,737,418.23                 5,368,709.12                $30,000
31
            21,474,836.47              10,737,418.24                $31,000
(Future Value)   Compounding interest calculator
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