One penny for your thoughts…and another penny tomorrow, the day after, etc.
What would happen if that lone penny was allowed to double every 24 hours for a month?
You may be surprised at how much growth can come from such humble beginnings.
Like most exponential adventures, it begins quite innocently.
A copper penny on the first day doesn’t seem like much, but what happens by the end of the month?
Let’s just say Scrooge McDuck might start to get nervous about the new competition in town.
Through the magic of daily compounding, our penny friend is about to embark on a life journey.
Join us on this financial roller coaster as we chart our meteoric rise from pauper to penny ale, one period at a time.
By the end of the month, these returns will impress even the most bullish stockbroker.
Grab your calculator, calculate the logarithmic scale, and get ready to watch your small investments pay off.
The only way out from here is up, up, and away as our pennies truly learn the power of exponential growth.
The final total may shock you, but the math doesn’t lie. let’s start! “
This is a graph showing how a penny doubles every day for a month.
Day | amount |
---|---|
1 | $0.01 |
2 | $0.02 |
3 | $0.04 |
Four | $0.08 |
Five | $0.16 |
6 | $0.32 |
7 | $0.64 |
8 | $1.28 |
9 | $2.56 |
Ten | $5.12 |
11 | $10.24 |
12 | $20.48 |
13 | $40.96 |
14 | $81.92 |
15 | $163.84 |
16 | $327.68 |
17 | $655.36 |
18 | $1,310.72 |
19 | $2,621.44 |
20 | $5,242.88 |
twenty one | $10,485.76 |
twenty two | $20,971.52 |
twenty three | $41,943.04 |
twenty four | $83,886.08 |
twenty five | $167,772.16 |
26 | $335,544.32 |
27 | $671,088.64 |
28 | $1,342,177.28 |
29 | $2,684,354.56 |
30 | $5,368,709.12 |
This happens because the chart shows the penny doubling every day for a month.
Here’s a breakdown of the reasons for the exponential growth:
- Day 1 starts at $0.01 (1 penny).
- On the second day, that penny doubles to $0.02.
- On the third day, $0.02 doubles again to $0.04.
- This pattern of doubling the previous day’s amount continues every day.
- When doubling a small amount, growth is slow at first
- But when the amount gets bigger by doubling over and over again, its growth accelerates exponentially
- This is because doubling incorporates the previous day’s increase, and the increases compound.
- This daily doubling process increased each penny to more than $5,300,000 by the end of the month.
- This shows that compound interest/growth has a powerful effect over time, even for small incremental changes each period.
To summarize, this exponential growth curve occurs because the penny doubles every day. This means that he doubles again the next day, incorporating the previous day’s growth into the new higher base amount.