Take a look at this article on HumbleDollar. You will find it enlightening and entertaining. Compounding is a powerful tool often underestimated by savers.
The message is simple, save even a little and save early to give your money as much time as possible to work for you.
Another example: Suppose you started with one penny on the first day of the month and then doubled it each day—to two cents, then four, then eight and so on.
The results are similar to the paper experiment: After 10 days, you’d have $5. After 20 days, you’d have $5,000 and, after 30 days, you’d have more than $5 million. While entertaining, these examples are so extreme that they’re of little practical value. But they carry an important lesson: The path to improvement in any domain does not require swing-for-the-fences, Herculean efforts. It requires only small steps done consistently. This is the meaning of “atomic habits.”
The problem is, we’re just not very good at doing compound calculations in our heads. We tend to think more linearly. Ask people to guess at the paper folding question, and typical answers will be in the range of three feet. Answers to the penny question normally fall in the range of $1,000. Unless you work out the math step by step, it’s very hard to make an estimate that’s anywhere close to correct.