Why the Doubling Penny Example Needs to Be Reevaluated
- Noah Avery
- Sep 29, 2023
- 2 min read
Updated: Jun 22, 2024
One of the most referenced examples of compound interest is the doubling penny example. It's often presented in a way where you're asked if you would take $1 million today, or have a penny double every day for 30 days. The purpose of people presenting the example is often to be in favor of choosing the doubling penny instead of the $1 million, but is it really the right choice?
Here's the math of the doubling penny over 30 days.
$.01
$.02
$.04
$.08
$.16
$.32
$.64
$1.28
$2.56
$5.12
$10.24
$20.48
$40.96
$81.92
$163.84
$327.68
$655.36
$1,310.72
$2,621.44
$5,242.88
$10,485.76
$20,971.52
$41,943.04
$83,886.08
$167,772.16
$335,544.32
$671,088.64
$1,342,177.28
$2,684,354.56
$5,368,709.12
Every time I see people reference this example, I see it represented in a month time frame, but their intention is to represent your financial choices over a lifetime. Because of this, let's translate every day of the 30 days into two years. This was we can see the doubling occur across a lifetime. For this example let's say when we start, we're at the age of 28 years old.
Year 0, 28 years old $.01
Year 2, 30 years old $.02
Year 4, 32 years old $.04
Year 6, 34 years old $.08
Year 8, 36 years old $.16
Year 10, 38 years old $.32
Year 12, 40 years old $.64
Year 14, 42 years old $1.28
Year 16, 44 years old $2.56
Year 18, 46 years old $5.12
Year 20, 48 years old $10.24
Year 22, 50 years old $20.48
Year 24, 52 years old $40.96
Year 26, 54 years old $81.92
Year 28, 56 years old $163.84
Year 30, 58 years old $327.68
Year 32, 60 years old $655.36
Year 34, 62 years old $1,310.72
Year 36, 64 years old $2,621.44
Year 38, 66 years old $5,242.88
Year 40, 68 years old $10,485.76
Year 42, 70 years old $20,971.52
Year 44, 72 years old $41,943.04
Year 46, 74 years old $83,886.08
Year 48, 76 years old $167,772.16
Year 50, 78 years old $335,544.32
Year 52, 80 years old $671,088.64
Year 54, 82 years old $1,342,177.28
Year 56, 84 years old $2,684,354.56
Year 58, 86 years old $5,368,709.12
As we can see, we don't cross the $1 million mark until we're over 80 years old. By this age, money may be worth 1/10 of what it was when we first stared because of inflation. You spent your whole life compounding that penny and the million now only has the buying power of $100,000 when you started.
So from this example, we can see that yes, doubling does lead to a large number. However, without a significant amount to start with, we spend our whole lives struggling. This example illustrates that it is very important to compound money. However, at the beginning stages of our financial careers, it is exponentially important to accumulate as much as we can so that we're not only doubling a penny.
