A Fable: Pennies a Day and the Power of Compounding

Once Upon a Time

there was a man of significant wealth and the father of seven children – six sons and a daughter. He resolved to teach them an important financial principle. On New Year’s Day the first of January, he made this offer to each of his children. They could chose a gift of:

  • A million dollars today – or –
  • A penny today that would double each day for the entire month of January.

The six sons immediately took the offer of a million dollars. However, the daughter, who was also the youngest, thought better and selected the second choice. As she accepted the penny, her older brothers laughed and ridiculed her.

At the end of the first week, the daughter received 64 cents, and her total received was $1.27. Her brothers could not even to begin to understand her stupid, foolish decision.

At the end of the second week, the daughter received $81.92, for a total of $163.83. Her older brothers were a bit surprised that that she had received over a hundred dollars so far, given that she had started out with just a single penny. Still, she had made a really dumb decision, they all agreed.

On the end last day of the third week, the daughter received $10,485.76, for a total of $20,971.51. Her older brothers were impressed by how her gifts had grown. Still, there was no possible way she could end up with more than a million dollars. They had definitely made the better choice.

However, at the end of of the fourth week, the daughter received $1,342,177.28 and a total of $2,684,354.55!!! The brothers were in a state of shock! The penny a day had grown to exceed a million dollars a day!

On the 31st of January, the daughter received her final gift of $10,737,418.24 for a grand total of $21,474,836.47. Her older (and now wiser) brothers had learned a hard and expensive lesson. This is the power of compounding.

This power of compounding is a fundamental principle for building  personal wealth over the long term. It is a call to diligently save and wisely invest.

Of course, doubling an investment day after day, or even year after year, is nigh impossible. However, doubling an investment over 8 to 15 years can be viable.

Even if you are young with just a modest amount to invest, remember that those ‘pennies a day’ can turn into quite a windfall in the decades to come.

So, how do you determine the time required for an investment to double? There is a simple formula to estimate the time, called the ‘Rule of 72’. The ‘Rule of 72’ details will be explained in an upcoming post.

Meanwhile get those pennies working today.

© 2016 Paul J Reimold

Here’s a day-by-day chart and table:

Pennies a Day Chart

 

Growth of Daughter’s Gift
Day of Month Gift Amount Total Gifts
1 $0.01 $0.01
2 $0.02 $0.03
3 $0.04 $0.07
4 $0.08 $0.15
5 $0.16 $0.31
6 $0.32 $0.63
7 $0.64 $1.27
8 $1.28 $2.55
9 $2.56 $5.11
10 $5.12 $10.23
11 $10.24 $20.47
12 $20.48 $40.95
13 $40.96 $81.91
14 $81.92 $163.83
15 $163.84 $327.67
16 $327.68 $655.35
17 $655.36 $1,310.71
18 $1,310.72 $2,621.43
19 $2,621.44 $5,242.87
20 $5,242.88 $10,485.75
21 $10,485.76 $20,971.51
22 $20,971.52 $41,943.03
23 $41,943.04 $83,886.07
24 $83,886.08 $167,772.15
25 $167,772.16 $335,544.31
26 $335,544.32 $671,088.63
27 $671,088.64 $1,342,177.27
28 $1,342,177.28 $2,684,354.55
29 $2,684,354.56 $5,368,709.11
30 $5,368,709.12 $10,737,418.23
31 $10,737,418.24 $21,474,836.47

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