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. |

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.

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.

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.

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)

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.

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 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.

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.

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.

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.

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.

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.

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.

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

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

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.

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,

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.

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.

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

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

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

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

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

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