A penny for your thoughts…and another penny tomorrow, the next day, and so on.
What happens when that lonely penny is allowed to double in on itself every 24 hours for an entire month?
You may be surprised at how much growth can come from such humble beginnings.
It starts innocently enough, as most exponential adventures do.
A single copper cent on day one doesn’t seem like much but by the end of the month?
Let’s just say Scrooge McDuck may start getting nervous about some new competition in town.
Through the magic of daily compounding interest, our penny friend is about to take the ride of its life.
Join us on this monetary rollercoaster as we chart the meteoric rise from pauper to penny-aire, one doubling period at a time.
By the month’s end, these returns will impress even the most bullish of stockbrokers.
So grab your calculators, break out the logarithmic scales, and get ready to watch tiny investments take off.
The only way from here is up, up, and away as our penny truly learns the power of exponential growth.
Its final total may shock you – but the math doesn’t lie. Let’s get started!”
Here is a chart illustrating how a penny doubled each day for a month grows:
| Day | Amount |
|---|---|
| 1 | $0.01 |
| 2 | $0.02 |
| 3 | $0.04 |
| 4 | $0.08 |
| 5 | $0.16 |
| 6 | $0.32 |
| 7 | $0.64 |
| 8 | $1.28 |
| 9 | $2.56 |
| 10 | $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 |
| 21 | $10,485.76 |
| 22 | $20,971.52 |
| 23 | $41,943.04 |
| 24 | $83,886.08 |
| 25 | $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, in the chart, the penny is doubling every day for a month.
Here’s a breakdown of why it grows exponentially:
- On day 1, you start with $0.01 (1 penny)
- On day 2, that penny doubles to $0.02
- On day 3, the $0.02 doubles again to $0.04
- This pattern of doubling the previous day’s amount continues each day
- When you double small amounts, the growth is slow at first
- But as the amounts get larger after doubling many times, the growth accelerates exponentially
- This is because doubling incorporates the previous day’s growth, so the increases build upon each other in a compounding manner.
- By the end of the month, a single penny has grown to over $5,3000,000 through this daily doubling process.
- This illustrates the powerful effect of compounding interest/growth over time, even with small incremental changes each period.
So, in summary, this exponential growth curve happens because the penny doubles every day, which means it is incorporating the previous day’s growth into a new higher baseline amount to double again the next day.
